SOLUTION: a boy on his bicycle intends to arrive at a certain time to a town that is 30 km away from his home . after riding 10 km, he rested for half an hour and as a result he was obliged

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Question 493396: a boy on his bicycle intends to arrive at a certain time to a town that is 30 km away from his home . after riding 10 km, he rested for half an hour and as a result he was obliged to ride the rest of the trip 2km/hr faster . what was his original speed ?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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a boy on his bicycle intends to arrive at a certain time to a town that is 30 km away from his home .
after riding 10 km, he rested for half an hour and as a result he was obliged to ride the rest of the trip 2km/hr faster .
what was his original speed?
:
Let s = his original speed
then
(s+2) = his faster speed
:
Write a time equation; Time = dist/speed
:
Required time = faster time + half an hr
30%2Fs = 30%2F%28%28s%2B2%29%29 + .5
multiply by s(s+2)
s(s+2)*30%2Fs = s(s+2)*30%2F%28%28s%2B2%29%29 + .5s(s+2)
:
Cancel the denominators
30(s+2) = 30s + .5s^2 + 1s
30s + 60 = 30s + .5s^2 + s
:
Arrange as quadratic equation on the right
0 =.5s^2 + 30s - 30s + s - 60
.5s^2 + s - 60 = 0
:
multiply by 2 (make the coefficient of s^2 = 1, easier to factor)
s^2 + 2s - 120 = 0
:
Factors to
(s+12)(s-10) = 0
:
the positive solution
s = 10 km/hr is his original speed
;
:
:
Check this by finding the actual time for each scenario
30/10 = 3hrs
30/12 = 2.5 hrs + half hr rest = 3hrs