It takes 36 minutes less time to travel 120 miles by car at night than by day because the lack of traffic allows the average speed at night to be 10 miles per hour faster than the daytime. Find the average speed in the daytime.

Question

Arthur

Mathematics

9 June, 13:14

It takes 36 minutes less time to travel 120 miles by car at night than by day because the lack of traffic allows the average speed at night to be 10 miles per hour faster than the daytime. Find the average speed in the daytime.

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Answers (1)

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Carla Dawson · Answer 1

Let the average speed at day time be x miles per hour

Therefore at night the average speed = (x + 10) miles per hour

Time = Distance / speed

Time at day - Time at night = 36 minutes.

36 minutes = 36/60 hour = 6/10 hour

Time at day = Distance / speed at day = 120 / x

Time at night = Distance / speed at night = 120 / (x + 10)

120/x - 120 / (x + 10) = 6/10

1/x - 1 / (x + 10) = 6/10 * 1/120

1/x - 1 / (x + 10) = 1/200

((x + 10) - x) / ((x) (x+10)) = 1/200

(x + 10 - x) / ((x) * (x+10)) = 1/200

10 / ((x) * (x + 10)) = 1/200

1 / ((x) * (x + 10)) = 1/2000

Therefore x (x + 10) = 2000

x and x + 10 are 40 and 50. Because 40*50 = 2000

x = 40

Average speed in the day time = 40 miles per hour