Question

To reach point b from point a, at 4 pm, sara will have to travel at an average speed of 18 kmph. She will reach point b at 3 pm if she travels at an average speed of 24 kmph. At what average speed should sara travel to reach point b at 2 pm?

Answer 1

Answer:

Let’s assume that Sara started her journey from point a at 1 p.m.

Therefore,  

If Sara’s average speed is 18 km/hr, she reaches the point b from a, at 4 p.m. i.e., t1 = 3 hrs [1 p.m. to 4 p.m. = 3 hours]

If Sara’s average speed is 24 km/hr, she reaches the point b from a, at 3 p.m. i.e., t2 = 2 hrs [1 p.m. to 3 p.m. = 3 hours]

The difference in the time taken by Sara is 1 hour.

Let the distance from point a to b be “x” kilometres.

Based on the question, we can write

t1 – t2 = 1 hour

or, x/18 – x/24 = 1

or, 4x – 3x = 72

or, x = 72 km

Now, we are given that Sara has to reach the point b at 2 p.m. i.e., t3 = 1 hour [1 p.m. to 2 p.m. = 1 hour]

So, corresponding to t1, the time difference of t3 and t1 will be 3 hours – 1 hour = 2 hours.

Let the average speed required by Sara to reach point b, at 2 p.m. be “S”  

Thus,  

t1 – t3 = 2 hours

or,  72/18 – 72/S = 2

or, 4 – 72/S = 2

or, 2 = 72/S

or, S = 72 / 2 = 36 km/hr

Hence, Sara should travel  at an average speed of 36 km/hr to reach point b at 2 pm.