SOLUTION: A cyclist after riding a certain distance stopped for half an hour to repair his machine after which he completes the whole journey of 30Km at half speed in 5 hours. If the breakdo

Question 974310: A cyclist after riding a certain distance stopped for half an hour to repair his machine after which he completes the whole journey of 30Km at half speed in 5 hours. If the breakdown has occurred 10Km further off, he would have done the whole journey in 4 hours.Find where breakdown occured and his original speed.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A cyclist after riding a certain distance stopped for half an hour to repair his machine after which he completes the whole journey of 30Km at half speed in 5 hours.
If the breakdown has occurred 10Km further off, he would have done the whole journey in 4 hours.
Find where breakdown occurred and his original speed.
:
let s = original speed
then
.5s = half speed
:
let d = that "certain distance" where the breakdown occurred
:
He rode d at original speed and (30-d) at half speed
:
Write a time equation, time = dist/speed
:
Time at full speed + repair time + time at half speed = 5 hrs
+ .5 + = 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
:
If the breakdown has occurred 10Km further off, he would have done the whole journey in 4 hours.
+ .5 + = 4
+ .5 + = 4
multiply by s
(d + 10) + .5s + 2(20-d) = 4s
d + 10 + .5s + 40 - 2d = 4s
d - 2d + .5s - 4s + 10 + 40 = 0
-d - 3.5s + 50 = 0
d + 3.5s - 50 = 0
d + 3.5s = 50
:
Use elimination with these two equations to find s
d + 4.5s = 60
d + 3.5s = 50
---------------Subtraction eliminates d
0 + 1s = 10
Original speed = 10 km/hr
Find d
d + 4.5(10) = 60
d + 45 = 60
d = 60 - 45
d = 15 km to the to breakdown
:
:
Check this in the statement
"If the breakdown has occurred 10Km further off, he would have done the whole journey in 4 hours.
+ .5 + =
2.5 + .5 + 1 = 4, confirms our solutions
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