Question

Two vehicles start from places P and Q towards Q and P respectively at the same time. After crossing eachother, they complete their journey in 7/2 hours and 18/7 hours respectively. If the second vehicle moves at aspeed of 70 km/h, then find the speed of the first vehicle.A)54 km/hB)48.6 km/hC)72 km/hD)60 km/h​

Answer 1

Given:

The speed of the second vehicle is 70 km/h

To find:

The speed of the first vehicle.

Solution:

1) Time taken to complete the journey by both vehicles after crossing each other is given, so there is a direct formula to find the speed.

• $\frac{s1}{s2} = \sqrt{\frac{t2}{t1} }$

s1 = speed of vehicle 1 = x

s2 = speed of vehicle 2 = 70

t1 = after crossing time taken by vehicle 1 to complete the journey. = 7/2

t2 = after crossing time taken by vehicle 2 to complete the journey. = 18/7

2) So the speed of the first vehicle is given by:

• $\frac{x}{70} =\sqrt{\frac{\frac{18}{7} }{\frac{7}{2} } }$

• $\frac{x}{70} =\sqrt{\frac{18.2}{7.7} }$

• $\frac{x}{70} ={\frac{6}{7} }$

• $x={\frac{6}{7} }.70$

• x = 60

The speed of the first vehicle is 60 km/h.