SOLUTION: 10. The bicycle club members left the campus to go to a park 24 km away for an outing. Manu left from the same place by car with picnic supplies 1 and a half hours later, travel

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Question 623239: 10. The bicycle club members left the campus to go to a park 24 km away for an outing. Manu
left from the same place by car with picnic supplies 1 and a half hours later, travelled at a
speed four times as fast and arrived at the park at the same time as the cyclists. How fast did
Manu drive ?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the bicycle club members
How much of a head start did the bicycle club members have?
+d%5B1%5D+=+s%2A1.5+ km
----------------
Start a stop watch when Manu leaves
Both he and the b.c.m. will travel for the same length of time
on the stop watch.
b.c.m. equation:
(1) +24+-+1.5s+=+s%2At+
Manu's equation:
(2) +24+=+4s%2At+
-----------------
(2) +t+=+6%2Fs+
Substitute this into (1)
(1) +24+-+1.5s+=+s%2A%286%2Fs%29+
(1) +24+-+1.5s+=+6+
(1) +1.5s+=+24+-+6+
(1) +1.5s+=+18+
(1) +s+=+12+
+4s+=+48+
Manu.s speed is 48 km/hr
check:
(2) +24+=+4s%2At+
(2) +48t+=+24+
(2) +t+=+.5+ hrs
and
(1) +24+-+1.5s+=+s%2A.5+
(1) +.5s+%2B+1.5s+=+24+
(1) +2s+=+24+
(1) +s+=+12+
OK