A cyclist after riding a certain distance ,stopped for half an hour to repair his bicycle, after which he completes the whole 30km at half speed in 5hours.if break down has occurec 10km farther off he would have done the whole journey in 4hr Find where the breakdown occured and orignal speed.
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then
.5s = half speed
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let d = that "certain distance" where the breakdown occurred
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He rode d at original speed and (30-d) at half speed
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Write a time equation, time = dist/speed
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Time at full speed + repair time + time at half speed = 5 hrs
d%2Fs + .5 + %28%2830-d%29%29%2F%28.5s%29 = 5
Multiply equation by s
d + .5s + 2(30-d) = 5s
d + .5s + 60 - 2d = 5s
combine like terms
d - 2d + .5s - 5s + 60 = 0
-d - 4.5s + 60 = 0
multiply by -1
d + 4.5s - 60 = 0
d + 4.5s = 60