SOLUTION: 1.) Jonathan drove his car from A to B at 81 km/hr. His car broke down and he returned by bus at 54 km/hr. his total travel was 5 hours. how long was his trip by car?

Question 472725: 1.) Jonathan drove his car from A to B at 81 km/hr. His car broke down and he returned by bus at 54 km/hr. his total travel was 5 hours. how long was his trip by car?
Found 2 solutions by monika_p, Theo:
Answer by monika_p(71) (Show Source): You can put this solution on YOUR website!
The speed formula is: v=d/t
You have given
speed from A to B v1=81km/hr
speed from B to A v2=54km/hr
total travel time t1+t2=5hr
the distance d from A to B and B to A is the same
Then
v1=d/t1 d=v1*t1
v2=d/t2 d=v2*t2
since distnce is same you compare 2 equations
v1*t1=v2*t2
81*t1=54*t2
Now use information about the time t1+t2=5hr ---> t1=5-t2 substitute and solve fo t2
81*(5-t2)=54*t2
405-81t2=54*t2
135*t2=405
t2=3hr then trip by car t1=2hr

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
his car presumably broke down when he was at B.
the formula to use for this type of problem is rate * time = distance.
let the distance between A and B equal d.
the time it took to get there and back = 5.
the rate to get there is 81 k/m.
the rate to get back is 54 k/m.
let h1 equal the hours it took to get there.
let h2 equal the hours it took to get back.
the rate * time formula to go from A to B is:
81 * h1 = d
the rate * time formula to go from B to A is:
54 * h2 = d
since they are both equal to d, then we can set each of these equations equal to each other, so we get:
81 * h1 = 54 * h2
we also know that:
h1 + h2 = 5
we can substitute for h1 by solving the equation for h1 by getting:
h1 = 5 - h2
substituting in the equation of:
81 * h1 = 54 * h2 gets us:
81 * (5 - h2) = 54 * h2
simplifying gets us:
(81 * 5) - (81 * h2) = (54 * h2)
adding (81 * h2) to both sides of this equation gets:
81 * 5 = (54 * h2) + (81 * h2) which becomes:
81*5 = 135*h2
dividing both sides of this equation by 135 gets:
h2 = 81*5/135 which becomes:
h2 = 3
this means that h1 = 2 because h1 + h2 = 5
we have:
h1 = 2
h2 = 3
it took 2 hours to get there by car.
it took 3 hours to get back by bus.
plug into rate * time = distance formula to get:
81 * 2 = 162
54 * 3 = 162
the distance was 162 kilometers each way.
the total travel time was 5 hours.
answer to the question is that the trip by car took 2 hours.

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