SOLUTION: Two cities are 73.5km apart. Vehicle A leaves one city at the same time vehicle B leaves the other. Find the speed of vehicle A if it travels 6.8 km/h faster than vehicle B and if

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Question 1094870: Two cities are 73.5km apart. Vehicle A leaves one city at the same time vehicle B leaves the other. Find the speed of vehicle A if it travels 6.8 km/h faster than vehicle B and if they pass in 17.3 minutes.
Found 2 solutions by KMST, MathTherapy:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= speed of B in km/h
x%2B6.8= speed of A in km/h

If A and B are traveling towards each other,
they will pass somewhere between the two cities.
That will happen in 17.3minutes or %2817.3minutes%29%2A%281hour%2F%2260+minutes%22%29=17.3%2F60hours .
At that time, the distances covered by each vehicle will be
%2817.3%2F60%29xkm for B, and %2817.3%2F60%29%28x%2B6.8%29km for A.
You can calculate an approximate decimal value for that 17.3%2F60=approximately0.28833 , and use it from now on
The sum of those distances is, of course, 73.5km, so the equation to solve is
%2817.3%2F60%29x%2B%2817.3%2F60%29%28x%2B6.8%29=73.5 .

Solving:
%2817.3%2F60%29x%2B%2817.3%2F60%29%28x%2B6.8%29=73.5
%2817.3%2F60%29%282x%2B6.8%29=73.5
%2860%2F17.3%29%2817.3%2F60%29%282x%2B6.8%29=73.5%2860%2F17.3%29
2x%2B6.8=73.5%2860%2F17.3%29
2x%2B6.8-6.8=73.5%2860%2F17.3%29-6.8
2x=73.5%2860%2F17.3%29-6.8
%281%2F2%292x=%281%2F2%29%2873.5%2860%2F17.3%29-6.8%29
x=73.5%2A30%2F17.3-3.4
The result of that calculation is
107309%2F865 or 124%2649%2F865 or approximately124.0566 .
So x=approximately124.0566 is the speed of B in km/h.
The speed of A, in km/h, is
x%2B6.8=approximately124.1%2B6.8=highlight%28130.9%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Two cities are 73.5km apart. Vehicle A leaves one city at the same time vehicle B leaves the other. Find the speed of vehicle A if it travels 6.8 km/h faster than vehicle B and if they pass in 17.3 minutes.
Let A's speed be S

Then B's speed = S - 6.8

Since distances they covered when they "met," sum to 73.5, we get the following DISTANCE equation: matrix%281%2C3%2C+%2817.3%2F60%29S+%2B+%2817.3%2F60%29%28S+-+6.8%29%2C+%22=%22%2C+73.5%29

17.3S + 17.3S - 17.3(6.8) = 60(73.5) ------ Multiplying by LCD, 60

34.6S = 60(73.5) + 17.3(6.8)

S, or A's speed = 

That's all! I hate working problems that don't have INTEGER solutions.