Question

A and B can both walk at a speed 2.4 m/s and run at a speed 5.5 m/s. They start off together to go a distance 65 m. A walks for one half of the time it takes him to reach the distance, and runs for the remaining half the time. B, on the other hand, walks for half the distance, and runs for the remaining half the distance. Calculate how much sooner will A reach the distance as compared to B.

Answer 1

3 seconds

Step-by-step explanation:

Total distance = 65 m

Walking speed of both the runners = 2.4 m/s

Running speed of both the runners = 5.5 m/s

Time taken for walking by A= t/2

Time taken while running by A = t/2

`d_1`= Walking distance

`d_2`= Running distance

Distance = Speed × Time

Time taken by A

`d=d_1+d_2\\\Rightarrow 65=2.4(t)/(2)+5.5(t)/(2)\\\Rightarrow 65* 2=7.9t\\\Rightarrow t=(130)/(7.9)=16.46\ s`

Time taken by A is 16.45 seconds

Distance B runs and walks = 65/2 = 32.5 m

`t=t_1+t_2\\\Rightarrow t=(d_1)/(v_1)+(d_2)/(v_2)\\\Rightarrow t=(32.5)/(2.4)+(32.5)/(5.5)\\\Rightarrow t=19.45\ s`

Time taken by B is 19.45 seconds

A will complete the distance 19.45-16.45 = 3 seconds before B