SOLUTION: A vehicle starts traveling from city A towards city B. It maintains a speed of 45 miles per hour. Another vehicle starts the same trip 45 minutes later going 70 miles per hour. Whe

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Question 893809: A vehicle starts traveling from city A towards city B. It maintains a speed of 45 miles per hour. Another vehicle starts the same trip 45 minutes later going 70 miles per hour. Where (a distance from city A) will the faster vehicle take over the slower one.
Found 3 solutions by josgarithmetic, MathTherapy, richwmiller:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Many examples like this are requested.

The described problem can be generalized like this:
A vehicle starts traveling from city A towards city B. It maintains a speed of r miles per hour.
Another vehicle starts the same trip k hours later going R miles per hour.
Where (a distance from city A) will the faster vehicle take over the slower one.
0%3Cr%3CR, and k%3E0.

Let d be the distance where the late fast car reaches the early slow car.
t is unknown,
d is unknown.

_________________speed________time_______distance
EARLY SLOW________r___________t+k_________d
LATE FAST_________R____________t__________d

EQUATIONS
r%28t%2Bk%29=d and Rt=d;
Solve for t and d.

Simply equating the two formulas for d,
r%28t%2Bk%29=Rt
rt%2Brk=Rt
rt%2Brk-Rt=0
rt-Rt=-rk
t%28r-R%29=-rk
t=-rk%2F%28r-R%29 and then multiply by %28-1%29%2F%28-1%29
highlight%28t=rk%2F%28R-r%29%29

Use this result for t in either of the original equations to find d.
d=Rt
d=R%28rk%2F%28R-r%29%29
highlight%28d=%28rRk%29%2F%28R-r%29%29, d, the distance completely in symbolic form.

Now you can simply substitute the values from the problem description for r, R, and k, and evaluate d.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A vehicle starts traveling from city A towards city B. It maintains a speed of 45 miles per hour. Another vehicle starts the same trip 45 minuets later going 70 miles per hour. Where (a distance from city A) will the faster vehicle take over the slower one.


Slower vehicle overtaken: highlight_green%28highlight_green%2894.5%29%29 miles from city A, heading to city B.

You can do the check!! 



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Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
vehicle A travels .75 *45=33.75 miles in 45 minutes before Vehicle B has started.
Vehicle B is going 70-45 =25 mph faster than vehicle A
so it will take B 33.75/25=1.35 hours to catch up
in 1.35 hours b goes 70*1.35=94.5 miles