Question

A cyclist rides from A to B at an average speed of 15km/h and returns back at an average speed of 20km/h.Find the average speed for the entire trip

Answer 1

A cyclist rides from A to B at an average speed of 15km/h and returns back at an average speed of 20km/h.

We have to find the average speed of the cyclist for the entire trip.

Now,

Average speed is defined as the ratio of total distance covered with respect to total time taken.

As the distance covered by the cyclist is same i.e. x km. From A to B distance covered is x km and from B to A distance covered is x km. So, the total distance covered by the cyclist is 2x km.

Also,

Time = Distance/Speed

t1 = x/15 hr and t2 = x/20 hr

Total time taken = t1 + t2

= x/15 + x/20

= x/15(1/3 + 1/4)

= x/5(7/12)

= 7x/60

Average speed = 2x/(7x/60)

= (2*60)/7

= 17.14

Therefore, the average speed of the cyclist for the entire trip is 17.14 km/hr.

Shortcut Method

Average speed = (2 × S1 × S2)/(S1 + S2)

= (2 × 15 × 20)/(15 + 20)

= 600/35

= 17.14 km/hr

Answer 2

GIVEN:

FIRST, from A to B

Average speed = 15km/hr

NOW, from B to A

Average speed = 20km/hr

TO FIND:

The average speed for the entire trip

SOLUTION:

The average speed for the entire trip= (15 + 20) ÷2

= 35/2

= 17.5 km/hr

= 17.5 km/hr OR

= 17.5 km/hr OR =17 ½ km/hr ANSWER☺

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