SOLUTION: Hi, I am studying for my Math Exam tomorrow. I was not sure how to set up the following problem for solving. Can you explain, please? Bob drove 200 miles in the same amount of

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Question 951840: Hi, I am studying for my Math Exam tomorrow. I was not sure how to set up the following problem for solving. Can you explain, please?
Bob drove 200 miles in the same amount of time that it took a propeller plane to fly 1,100 miles. The speed of the plane was 180 mph faster than the speed of the car. Find the speed of thee car and the speed of the plane.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Bob drove d%5B1%5D=200mil in the same amount of time t that it took a propeller plane to fly d%5B2%5D=1100mil
d%5B1%5D=200mil in time t%7D%7D+is%3A%0D%0A%0D%0A%7B%7B%7Bd%5B1%5D=s%2At
speed+=s+%28mil%2Fh%29
a propeller plane to fly:

d%5B2%5D=1100mil in same time t:
d%5B2%5D=s%2At
since given that the speed of the plane was 180%28mil%2Fh%29 greater then speed of a car, we have
speed+=%28s+%2B180%29%28mil%2Fh%29
now we have for the car:
200mil=s%28mil%2Fh%29%2At
and the plane:
1100mil=%28s+%2B180%29%28mil%2Fh%29%2At
since given that t equal, we have
t=200mil%2Fs%28mil%2Fh%29....the car
and
t=1100mil%2F%28s+%2B180%28mil%2Fh%29%29.......the plane
so,
200mil%2Fs%28mil%2Fh%29=1100mil%2F%28s%28mil%2Fh%29+%2B180%28mil%2Fh%29%29 ...simplify

2%2Fs=11%2F%28s+%2B180%28mil%2Fh%29%29
2%28s+%2B180%28mil%2Fh%29%29=11s
2s+%2B360%28mil%2Fh%29=11s
360%28mil%2Fh%29=11s-2s
360%28mil%2Fh%29=9s
s=360%28mil%2Fh%29%2F9
s=highlight%2840%28mil%2Fh%29%29.....the speed of car
s+%2B180%28mil%2Fh%29=40%28mil%2Fh%29+%2B180%28mil%2Fh%29=highlight%28220%28mil%2Fh%29%29.....the speed of plane
check:
car
t=200mil%2Fs
t=200mil%2F40%28mil%2Fh%29
t=5h
plain
t=1100mil%2F%28s+%2B180%28mil%2Fh%29%29
t=1100mil%2F%28220%28mil%2Fh%29%29
t=5h
so, the time is same
your answer is:
the speed of car is highlight%2840%28mil%2Fh%29%29 and the speed of plane is highlight%28220%28mil%2Fh%29%29



Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Hi, I am studying for my Math Exam tomorrow. I was not sure how to set up the following problem for solving. Can you explain, please?
Bob drove 200 miles in the same amount of time that it took a propeller plane to fly 1,100 miles. The speed of the plane was 180 mph faster than the speed of the car. Find the speed of thee car and the speed of the plane.
Let speed of car be S

Then speed of plane = S + 180

Time car takes to travel 200 miles: 200%2FS

Time plane takes to travel 1,100 miles: 1100%2F%28S+%2B+180%29

Since times are equal, we get: 200%2FS+=+1100%2F%28S+%2B+180%29

1,100S = 200(S + 180) -------- Cross-multiplying

1,100S = 200S + 36,000 

1,100S – 200S = 36,000

900S = 36,000

S, or speed of car = 36000%2F900, or highlight_green%2840%29 mph

Speed of plane: 40 + 180, or highlight_green%28220%29 mph