car(a)50mph passes car(b)0mph car b waits 10sec then accels to 100mph in 30sec how long b4 b catches a?10+30+?

Question

10 sec wait + 30 sec accel + ?=?

Answer 1

The average speed during acceleration is 50 mph so the cars do not move apart from each other during this 30 second time.

Car A is traveling 50mph faster than car B for 10 seconds. After the acceleration Car B is traveling 50mph than Car A. It will take Car b 10 seconds to catch up.

Total time is 50 seconds.

Answer 2

Sa = 50(10/3600 + t)
Sb = (1 / 2)(100)(3600) / 30)(30 / 3600)^2 + 100(t - 30 / 3600) = Sa
(1/2)(100)(120)(1/120)^2 + 100(t - 1/120) = 50(1/360 + t)
(1/2)(100)/120 + 100t - 10/12 = 5/36 + 50t
50t = 5/36 + 5/6 - 5/12
50t = 5/36 + 30/36 - 15/36
t = (2/180 hr)(60 min/hr)(60 sec/min)
t = 40 seconds