SOLUTION: Two small planes start from the same point and fly in opposite directions. The first plane is flying 25kph slower than the second plane. In 2 hours, the planes are 470 km apart. Fi

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Question 1011809: Two small planes start from the same point and fly in opposite directions. The first plane is flying 25kph slower than the second plane. In 2 hours, the planes are 470 km apart. Find the rate of each plane.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
Solved in generalized manner because the type of question is very frequent.
KNOWN VARIABLES: k, t, d
UNKNOWN: r
                   rate        time         distance
firstplane         r-k         t
secondplane        r           t
Total                                        d

                  rate        time         distance
firstplane         r-k         t           (r-k)t
secondplane        r           t            rt
Total                                        d

%28r-k%29t%2Brt=d
rt-kt%2Brt=d
2rt-kt=d
2rt=d%2Bkt
highlight%28r=%28d%2Bkt%29%2F%282t%29%29

Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!

Two small planes start from the same point and fly in opposite directions. The first plane is flying 25kph slower than the second plane. In 2 hours, the planes are 470 km apart. Find the rate of each plane.
Let slower plane's speed be S

Then faster plane's speed = S + 25

Two hours after takeoff, the sum of their speeds is: 470%2F2, or 235 km/h

We then get: S + S + 25 = 235

2S = 235 - 25

2S = 210

S, or speed of slower plane = 210%2F2, or highlight_green%28105%29 km/h

Speed of faster plane: 105 + 25, or highlight_green%28130%29 km/h