Word Problem.. intermediate word problem?

First you should assign the original speed to be the variable V.

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Next you assign each expression of speed a formula based on V.

Kim's initial speed = V

Kim's second speed = V - 15

Maria's average speed = V + 5

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Next you need to determine how long each person was traveling at each speed.

Kim's travel time = 3 hours at initial speed, 3 hours at second speed

Maria's travel time [2pm is 14:00] = 14:00 - 9:00 = 5 hours at average speed

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Now we determine the distance traveled by each woman.

Kim = (Initial speed)*(time at initial speed) + (second speed)*(time at second speed) =

= (V)*(3) + (V-15)*(3) =

= 3V + 3V - 15 =

= 6V - 15

Maria = (average speed)*(time at average speed) =

= (V+5)*(5) =

= 5V + 25

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Because we know they both traveled the same distance, the above two expressions are equal. All we have to do is solve for V:

6V - 15 = 5V + 25 <-- subtract 5V from both sides

V -15 = 25 <-- add 15 to both sides

V = 40 km/hour is Kim's original speed

.: QED 40 km/hour is Kim's original speed.

EDIT: No problem n_n pleasure to be of help.

It might help to think about the problem "backwards," with some numbers attached. If I told you that the car drove 680 miles, how many "340s" is that? 680/340 = 2, so there are two 340s, which equates to 2 hours with the lawn mower. In general then, to find the number of 340s in a given number of miles, you would divide the number of miles driven by 340. So in general H = x/340.