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# how to solve this

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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?

Jul 26, 2020

#1
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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.

Jul 26, 2020
#2
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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.

,

Jul 26, 2020