SOLUTION: two towns T and S are 300km apart. Two busses A and B Started from T at the same time travelling towards S. Bus B travelling at an average speed of 10km/hr greater than that of A r

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Question 1100999: two towns T and S are 300km apart. Two busses A and B Started from T at the same time travelling towards S. Bus B travelling at an average speed of 10km/hr greater than that of A reached S One and a quarter hours earlier.
i) find the average speed of A ?
ii) how far was A from T When B reached S ?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
BUS          SPEED     TIMES          DISTANCE
A            r         300/r           300
B            r+10      300/(r+10)      300
DIFFERENCE             1%261%2F4



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Bus B travelling at an average speed of 10km/hr greater than that of A reached S One and a quarter hours earlier.
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300%2Fr-300%2F%28r%2B10%29=1%261%2F4
-
300%2Fr-300%2F%28r%2B10%29=5%2F4
60%2Fr-60%2F%28r%2B10%29=1%2F4
240%2Fr-240%2F%28r%2B10%29=1
240r%2B2400-240r=r%5E2%2B10r-----------
r%5E2%2B10r-2400=0

r=%28-10%2Bsqrt%289700%29%29%2F2
r=%28-10%2B10%2Asqrt%2897%29%29%2F2
r=-5%2B5%2Asqrt%2897%29


highlight_green%28r=44.2%29 km%2Fhour

Answer by ikleyn(52890) About Me  (Show Source):
You can put this solution on YOUR website!
.
300%2Fr - 300%2F%28r%2B10%29 = 11%2F4


300%2Fr - 300%2F%28r%2B10%29 = 5%2F4

60%2Fr - 60%2F%28r%2B10%29 = 1%2F4

240%2Fr-240%2F%28r%2B10%29 = 1

240r + 2400 - 240r = r%5E2%2B10r

r%5E2%2B10r-2400 = 0

r%5B1%2C2%5D = %28-10+%2B+sqrt%289700%29%29%2F2

r%5B1%2C2%5D = %28-10%2B10%2Asqrt%2897%29%29%2F2 = -5+%2B-+5%2Asqrt%2897%29


i)   The speed of the bus A   r = -5+%2B+5%2Asqrt%2897%29 = 44.244 km/h.


ii)  The distance under the question = r%2A%285%2F4%29 = 44.244%2A%285%2F4%29 = 55.305 km.

Solved and answered.