Problems on Calculating Speed

Here we will learn to solve different types of problems on calculating speed.

We know, the speed of a moving body is the distance traveled by it in unit time.

Formula to find out speed = distance/time

Word problems on calculating speed:

1. A man walks 20 km in 4 hours. Find his speed.

Solution:

Distance covered = 20 km

Time taken = 4 hours

We know, speed = distance/time

= 20/4 km/hr

Therefore, speed = 5 km/hr

2. A car covers a distance of 450 m in 1 minute whereas a train covers 69 km in 45 minutes. Find the ratio of their speeds.

Speed of car = Distance covered/Time taken = 450/60 m/sec = 15/2

= 15/2 × 18/5 km/hr

= 27 km/hr

Distance covered by train = 69 km

Time taken = 45 min = 45/60 hr = 3/4 hr

Therefore, speed of trains = 69/(3/4) km/hr

= 69/1 × 4/3 km/hr

= 92 km/hr

Therefore, ratio of their speed i.e., speed of car/speed of train = 27/92 = 27 : 92

3. Kate travels a distance of 9 km from her house to the school by auto-rickshaw at 18 km/hr and returns on rickshaw at 15 km/hr. Find the average speed for the whole journey.

Time taken by Kate to reach school = distance/speed = 9/18 hr = 1/2 hr

Time taken by Kate to reach house to school = 9/15 = 3/5 hr

Total time of journey = (1/2 + 3/5) hr

Total time of journey = (5 + 6)/10 = 11/10 hr

Total distance covered = (9 + 9) km = 18 km

Therefore, average speed for the whole journey = distance/speed = 18/(11/10) km/hr

= 18/1 × 10/11 = (18 × 10)/(1 × 11) km/hr

= 180/11 km/hr

= 16.3 km/hr (approximately)

Speed of Train

Relationship between Speed, Distance and Time

Conversion of Units of Speed

Problems on Calculating Distance

Problems on Calculating Time

Two Objects Move in Same Direction

Two Objects Move in Opposite Direction

Train Passes a Moving Object in the Same Direction

Train Passes a Moving Object in the Opposite Direction

Train Passes through a Pole

Train Passes through a Bridge

Two Trains Passes in the Same Direction

Two Trains Passes in the Opposite Direction

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## Speed word problems

## Interesting speed word problems

Solution: The formula to get the average speed is

The total distance is 45 meters, so d = 45 meters.

It took the lion 5 seconds to reach a distance of 45 meters.

The total time is 5 seconds, so t = 5.

Just plug these into the formula.

You could also write d = 9 m/s.

Some possible instantaneous speed for the lion could be the followings:

13 meters in 1 second v = 13 m/s

9 meters in 1 second v = 9 m/s

10 meters in 1 second v = 10 m/s

8 meters in 1 second v = 8 m/s

5 meters in 1 second v = 5 m/s

As you can see the total distance is 13 + 9 + 10 + 8 + 5 = 45

and the total time is 1 + 1 + 1 + 1 + 1 = 5

## Challenging speed word problems

Second, it is convenient to convert miles per half hour to miles per hour.

35 miles per half hour is 70 miles per hour.

Lastly, convert the formula from speed to distance.

Now, we have the speed and the time, we can get the distance.

## Take a look also at the speed word problem below

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## Distance, Time and Speed Word Problems | GMAT GRE Maths

Problems involving Time, Distance and Speed are solved based on one simple formula.

Distance = Speed * Time

Distance covered = 4*40 = 160 miles

Let us see how this question can be solved.

For these kinds of questions, a table like this might make it easier to solve.

Let the distance covered by that person be ‘d’.

Walking at 4 mph and covering a distance ‘d’ is done in a time of ‘d/4’

IF he walks at 9 mph, he covers 7.5 miles more than the actual distance d, which is ‘d+7.5’.

He does this in a time of (d+7.5)/9.

Since the time is same in both the cases →

d/4 = (d+7.5)/9 → 9d = 4(d+7.5) → 9d=4d+30 → d = 6.

Here, we see that the distance is same.

Let us assume that its usual speed is ‘s’ and time is ‘t’, then

s*t = (1/3)s*(t+30) → t = t/3 + 10 → t = 15.

So the actual time taken to cover the distance is 15 minutes.

## Solved Questions on Trains

Let the time after which they meet be ‘t’ hours.

Then the time travelled by second train becomes ‘t-2’.

Distance covered by first train+Distance covered by second train = 320 miles

Let the speed of the first train be ‘s’.

Distance covered by the first train in (2+4) hours = Distance covered by second train in 4 hours

So the slower train is moving at the rate of 40 mph.

## Questions on Boats/Airplanes

For problems with boats and streams,

Similarly, for airplanes travelling with/against the wind,

Speed of the plane with the wind = speed of the plane + speed of the wind

Speed of the plane against the wind = speed of the plane – speed of the wind

Let the distance be ‘d’ miles.

Time taken to cover the distance upstream + Time taken to cover the distance downstream = 3

Speed downstream = 3+1 = 4 mph

Let the speed of the plane be ‘a’ and that of the wind be ‘w’.

4(a+w) = 2400 and 6(a-w) = 2400

Expressing one unknown variable in terms of the other makes it easier to solve, which means

Substituting the value of w in the second equation,

The speed of the plane is 500 kmph and that of the wind is 100 kmph.

## More solved examples on Speed, Distance and Time

Let the time taken by the train be ‘t’. Then that of bus is ‘3-t’.

The entire distance covered was 100 miles

Substituting the value of t in 40(3-t), we get the distance travelled by bus is 40 miles.

Alternatively, we can add the time and equate it to 3 hours, which directly gives the distance.

From the first equation, d=100t

The second equation is 630-d = 110(6-t).

Substituting the value of d from the first equation, we get

The time is ‘t’ for both of them because when they meet, they would have walked for the same time.

Since time is same, we can equate as

Solving this gives d=60/7 miles (8.5 miles approximately)

So the two persons meet after 2 6/7 hours.

## Practice Questions for you to solve

A) 30 kmph B) 20 kmph C) 15 kmph D) 40 kmph

Let the speed of the boat be ‘s’ kmph.

Then, 2(s+4) = 3(s-4) → s = 20

A) 30 miles B) 35 miles C) 40 miles D) 180 miles

Solving this gives d = 40 miles

## 17 thoughts on “Distance, Time and Speed Word Problems | GMAT GRE Maths”

Could you explain how ? you have two equations and there are 3 variables.

Speed comes out to be 20 km/hr and the time taken is 3 hrs. The distance traveled is 60 km.

(s + 4) (t – 1/2)= st 1…new equotion = -1/2s + 4t = 2

(s – 2) (t + 1/3)= st 2…new equotion = 1/3s – 2t = 2/3

st or distance = 3 x 20 = 60 km/h

Time taken by Meenu => t1 = 48/s Time taken by Priya => t2 = 72/(s+4)

t1=t2 Thus, 48/s = 72/(s+4) => 24s = 192 => s = 8Km/hr

Let speed of the CAR BE x kmph.

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## Speed Distance Time Video

https://youtu.be/rQUwNC0gqdg?t=2557

## Contrast with velocity

Speed is different from velocity, the latter has direction. Here's why that changes things:

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