Time Speed Distance Questions On Quant

We all know that speed is distance travelled by time taken. The problems of speed usually involves something or someone moving at a constant or average speed, and out of the three quantities (speed/distance/time), we are required to find out the missing one. However information regarding the other two will be provided in the question stem.

You might already be familiar with the formula

Distance = Speed X Time

Here, distance = [Speed x Time] formula is just a way of saying that the distance we travel depends on the speed we go for any length of time. For example if you travel at 50 mph for one hour, then you would have traveled 50 miles. If you travel for 2 hours at that speed, you would have traveled 100 miles. 3 hours would be 150 miles, etc. Now, if we were to double the speed, then you would have traveled 100 miles in the first hour and 200 miles at the end of the second hour. 

In other words, we can figure out any one of the components by knowing the other two. For example, if you have to travel a distance of 100 miles, but can only go at a speed of 50 mph, then you know that it will take you 2 hours to get there. Similarly, if a friend visits you from 100 miles away and tells you that it took him 4 hours to reach, you will know that he averaged at 25 mph.

Now let’s do a problem using the formula to understand better.

Time Speed Distance | Illustrative Example

Walking at 3/4 of his normal speed, Mike is 16 minutes late in reaching his office. The usual time taken by him to cover the distance between his home and his office is

A. 42 min

B. 48 min

C. 60 min

D. 62 min

E. 66 min

SOLUTION

Let, Distance to work = D miles

Normal time = t min (to find)  

Speed = s miles/min

Now, D =s×t ( in other days)

D = 34s×(t+16)

Equating the two 

s×t=34s×t+16

s×t=34s×t+16

4×t=3×t+16

t = 48 min  

Hence answer is B.

Average Speed

It’s very important to remember that Average speed is not average of speed but Average Speed= total distance travelled / total time taken

Let’s understand this with an example

Illustrative Example

A travels from A to B with a speed of 40 mph and return from B to A with a speed of 60 mph, what is the average speed?

SOLUTION

Let D =  distance from A to B 

And SAB = Speed from A to B; SBA = Speed from B to A

Time taken for A to B = DSAB 

Time taken from B to A = DSBA  

Average speed = 2 ×DDSAB+DSBA=2 ×DD40+D60=2 ×40×6040+60=48mph 

Now let’s do a problem to understand average speed better.

Try this Time Speed and Distance Problem

Tom traveled the entire 90 km trip. If he travelled the first 18 km of the trip at a constant rate of 36 km per hour and the remaining trip at a constant rate of 72 km per hour, what is his average speed? 

A. 30 km/h

B. 36 km/h

C. 45 km/h

D. 48 km/h

E. 60 km/h

SOLUTION

Time for the first part of the Journey =  18 km36 kmph = 0.5 hour  

Time for the Second part of the Journey = 90-18 km72 kmph= 1 hour 

Average Speed = Total distance Travelled/Total time taken=901.5=60 kmph

Answer is E.

Key take-aways

1. Use the simple formula Speed = Distance / Time to solve for unknown speed, time or distance.
2. Do not assume that average speed works the same way as normal averages for numbers do.
   Remember: Average speed = Total distance / total time
3. Be methodical. On the GMAT / GRE / SAT, even if a questions looks quite simple on the surface there might be hidden layers of complexity that you will miss if you aren’t diligent with your steps and though process.

Good Luck!