SOLUTION: The first car is going 40mi/h,and the second car is going 55mi/h.the first car left 3 hours before the second car.what equation could you use to find how many hours it will take fo

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Question 1059638: The first car is going 40mi/h,and the second car is going 55mi/h.the first car left 3 hours before the second car.what equation could you use to find how many hours it will take for the second car to catch up to the first car?
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
Typical traveling rates catchup problem. 

                SPEEDS        TIMES       DISTANCES
SLOW EARLY       40           t+3           d
FAST LATE        55            t            d



PURELY IN VARIABLES

                SPEEDS        TIMES       DISTANCES
SLOW EARLY       r            t+h           d
FAST LATE        R             t            d

system%28r=40%2CR=55%2Ch=3%29

system%28r%28t%2Bh%29=d%2CRt=d%29

r%28t%2Bh%29=Rt
rt%2Brh=Rt
Rt-rt=rh
%28R-r%29t=rh
highlight%28t=%28rh%29%2F%28R-r%29%29

Use the given values to evaluate time t.

Answer by ikleyn(53763) About Me  (Show Source):
You can put this solution on YOUR website!
.
The first car is going 40 mi/h,and the second car is going 55 mi/h.the first car left 3 hours before the second car.
what equation could you use to find how many hours it will take for the second car to catch up to the first car?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Everything is in these 4 lines below. 

Time to catch = %283%2A40%29%2F%2855-40%29 = 120%2F15 = 8 hours.

The numerator 3*40 = 120 kilometers is the distance for the first car to be ahead at the moment the second car started.


The difference (55-40) in the denominator is the rate of decreasing the distance between two cars. 
It is their relative speed.


That's all.

You should be able to write such an equation instantly as you read and understand the problem.

Producing tables is not the way solving such problems.


Answer by MathTherapy(10809) About Me  (Show Source):
You can put this solution on YOUR website!

The first car is going 40mi/h,and the second car is going 55mi/h.the first car left 3 hours before the second car.what equation could you use to find how many hours it will take for the second car to catch up to the first car?
With T being time for the faster to catch up to the slower car, we get the following DISTANCE equation: 40(T + 3)  = 55T

Solve this to get: highlight_green%28matrix%281%2C4%2C+T%2C+%22=%22%2C+8%2C+hours%29%29

That's all.....NOTHING COMPLEX!!