A car sets out from a service station travelling at 70 km/h. 22 minutes later a

Question

A car sets out from a service station travelling at 70 km/h. 22 minutes later a second car leaves the station travelling at 90 km/h in the same direction. How long does it take for the second car to catch up with the first?

A) 40.0 minutes B) 51.3 minutes C) 64.0 minutes D) 78.0 minutes E) 77.0 minutes

A rock is thrown with an initial speed of 12 m/s and at an angles 20oabove the horizontal. How far does the rock travel before returning to the same height at which it was thrown?

A) 9.4 m

B) 17.3 m

C) 6.3 m

D) 4.9 m

E) 5.1 m

Explanation / Answer

a) t = 77 minutes

First car travels for 22 minutes before second car leaves.

Let both cars meet after time 't' minutes after 2nd car started.

Speed of first car in km/min = 70*60 km/min

Speed of 2nd car in km/min = 90*60 km/min

After time t, first car travelled a distance = 70*60*22 + 70*60*t

After time t, second car travlled a distance = 90*60*t

They will meet when distances are equal.

=> 70*60*22 + 70*60*t = 90*60*t

=> 70*22 + 70t = 90t

=> 20t = 70*22

=> t = 22*7/2

=> t = 11*7

=> t = 77 minutes

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