Two cars are traveling north along a highway. The first drives at 40 mph, and the second, which leaves 3 hours later, travels at 60 mph. How long after the second car leaves will it take for the second car to catch the first?

Guest Jul 26, 2020

#1**0 **

Let the time taken by the first car =T

Distance =Time x speed

40T = 60*(T - 3)

40T =60T - 180

60T - 40T = 180

T = 9 hours for the first car, or:

9 - 3 = 6 hours for the second car - when it catches up with the first car.

Check: 40 mph x 9 hours =60 mph x 6 hours =360 miles covered.

Guest Jul 26, 2020

#2**0 **

*Two cars are traveling north along a highway. The first drives at 40 mph, and the second, which leaves 3 hours later, travels at 60 mph. How long after the second car leaves will it take for the second car to catch the first?*

Observe that "catch the first" car means "reach the same distance".

Distance equals velocity x time. S = v • t

1st car will travel this distance: S = 40 mph • H hours

2nd car will travel this distance S = 60 mph • (H – 3) hours

Since the 2nd car catches up with the 1st and that's the same as saying they've traveled the same distance, then set the distances equal.

40 mi/hr • H hr = 60 mi/hr • (H – 3) hr

Drop the units for ease 40H = 60H – 180

Subtract 60H from both sides –20H = –180

Divide both sides by –20 H = 9

Since we were talking about time,

then the applicable units is Hours The 2nd car catches the 1st car after **9 hours**

Check answer Does 40 • 9 = 60 • 6 ? Yes, it does.

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Guest Jul 26, 2020