SOLUTION: at 9 am, mark and tom get on their motor bikes to meet each other from towns located 45 km apart. mark travels 5 km/h faster than tom. at what must each travel if they were to meet

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Question 1012536: at 9 am, mark and tom get on their motor bikes to meet each other from towns located 45 km apart. mark travels 5 km/h faster than tom. at what must each travel if they were to meet at 10:12 am?
Found 2 solutions by ikleyn, fractalier:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
at 9 am, Mark and Tom get on their motor bikes to meet each other from towns located 45 km apart.
Mark travels 5 km/h faster than Tom. At what must each travel if they were to meet at 10:12 am?
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Let x be Mark' speed in . Then tom' speed is x-5 

Since they move toward each other, the rate of decreasing the distance between them is x + (x-5) = 2x-5 .

The time they spent for their trip is 1 hour 12 minutes, or  of an hour.

Your equation is Time = ,   or

 = .

To solve it, multiply both sides by 2x-5. You will get

6*(2x-5) = 5*45,   or

12x - 30 = 225,

12x = 225 + 30 = 255.

x =   = 21.25 .


Answer by fractalier(6550)   (Show Source): You can put this solution on YOUR website!
In general, remember rate times time equals distance.
Let us call Tom's rate, r.
Then Mark's rate is r+5.
The time they travel is an hour and twelve minutes...that's an hour and a fifth, or 6/5 hours.
The total distance they cover is 45 km.
Thus we can write
(6/5)r + (6/5)(r+5) = 45
Now solve this...maybe multiply everything by 5 to clear fractions...we get
6r + 6(r+5) = 225
6r + 6r + 30 = 225
12r + 30 = 225
12r = 195
r = 195/12 = 16.25 km/h
r+5 = 21.25 km/h
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