SOLUTION: Paula ran to Hugo in 6 hours, while Busking walked the same distance in 72 hours. How fast did Paula run if her speed was 11 kilometers per hour faster than Busking's? How far wa

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Question 1202546: Paula ran to Hugo in 6 hours, while Busking walked the same distance in 72 hours. How fast did Paula run if her speed was 11 kilometers per hour faster than Busking's? How far was it to Hugo?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
                          SPEED         TIME    DISTANCE

Paula to Hugo              d/6          6        d

Busking                    d/72        72        d

DIFFERENCE                 11

-----solve this for d.
Answer by ikleyn(52884)   (Show Source): You can put this solution on YOUR website!
.
Paula ran to Hugo in 6 hours, while Busking walked the same distance in 72 hours.
(a) How fast did Paula run if her speed was 11 kilometers per hour faster than Busking's?
(b) How far was it to Hugo?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let x be the rate of Paula, in kilometers per hour.

Then the Busking rate is (x-11) km/h.


The distance is the same; therefore, we can write a distance equation

    6x = 72(x-11)  kilometers.


Simplify and find the Paula's rate running

    6x = 72x - 72*11

    72*11 = 72x - 6x

    72*11 =    66x


Divide both sides by 11

    72 = 6x


Divide both sides by 6

     12 = x.


Thus, the Paula's rate running is 12 km/h.

It is the answer to question (a).


The distance to Hugo is  (the Paula's time * the Paula's rate) = 6*12 = 72 kilometers.

It is the answer to question (b).

Solved.



Answer by greenestamps(13209)   (Show Source): You can put this solution on YOUR website!


The ratio of the times is 6:72 = 1:12. Since the distances are the same, the ratio of the speeds is 12:1. Using that ratio of speeds,

Let x = Busking's speed
Then 12x = Paula's speed

Paula's speed was 11 km/h faster than Busking's:

12x - x = 11
11x = 11
x = 1

ANSWERS:

Paula's speed was 12x = 12 km/h
The distance to Hugo was (12 km/h)*(6h) = 72 km
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