Weekend Speed-Time Puzzle 2?

Question

Car A begins to drive from the town to the airport at 9.00 am at x km/hr
Car B begins to drive from the airport to the town at 9.17 am at y km/hr

After they pass each other, car A takes 10 minutes to reach the airport, while car B takes 20 minutes to reach the town.

the question is: At what time do the cars pass each other ?

note:
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This isn't a difficult problem, BA will be given to the SIMPLEST correct solution.

J · Accepted Answer

if T = time for A for the distance town-airport
elapsed time to meet B = T-10

T-10 = 17 + T'-20
T = T'+7
with T' = time for B for the distance airport-town

10x + 20y = D
with D = distance town-airport

x = D/T | y = D/T'

20D/T' + 10D/T = D
20/T' + 10/T = 1

20/T' + 10/(T'+7) = 1
==>T' = 28 and T = 35

T-10 = 25 minutes

at time : 9:25 am ..........answer

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Julius N · Answer

if car A leaves town at 9:00 am and it takes it 10 minutes to get to the airport then it will be at the airport at 9:10.

since car B doesn't leave the airport until 9:17, they won't really be passing each other.
They will be sitting next to each other from 9:10 , when car A arrives, until 9:17 when car B leaves.

oops, thank you M3 for pointing that out. My students do it all the time - they misread a problem and solve the problem they read instead of the one I made up.

OK, let's do it again. The distance traveled in time t by A equals the distance traveled in 20 minutes by B.
also, the distance traveled by A in 10 minutes equals the distance traveled by B in t-17 minutes.

so xt = 20y and 10x = (t-17)y
so x  = 20y/t and x = (t-17)y/10
so 20/t = (t-17)/10
so 200 = t2 - 17t 
and t = 25
so they meet at 9:25

never mind,  I see J already got the answer.

Julius

Weekend Speed-Time Puzzle 2?

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