To cover a distance of 40 km, A takes 2 hours more than B. If A doubles his speed, it takes him 1 (1/2) hours more than B to cover a distance of 80km. To cover a distance of 90 km, how long will B take at the same speed?
Answers
Step-by-step explanation:
Given :
Distance = 40 km
A takes 2 hrs more than B to cover 40 km
A takes 1.5 hrs more than B to cover 80 km
To find :
Time taken by B to cover 90 km
Formula used :
Distance = speed × time
Solution :
Let the speed of B be x kmph
⇒ Time taken by B to cover 40 km = 40/x
⇒ Time taken by A = (40/x) + 2
So, the speed of A = (20x)/(20 + x) ----(1)
Now,
Distance = 80 km
⇒ Time taken by B to cover 80 km = 80/x ----(2)
⇒ Speed of A when he doubles his speed = (40x)/(20 + x)
⇒ Time taken by A to cover 80 km = (40 + 2x)/(x) ----(3)
A.T.Q.,
From (2) and (3)
(80/x) + (3/2) = (40 + 2x)/x
⇒ 2 (40 + 2x - 80) = 3x
⇒ 2 (2x - 40) = 3x
⇒ 4x - 80 = 3x
⇒ 4x - 3x = 80
⇒ x = 80
⇒ Speed of B = 80 kmph
Distance = 90 km
Time taken by B = 90/80
∴ time taken by B to cover 90 km is one whole one by eight hrs.