Question 57268: ok i worked this problem and got the right answer but only by guessing. I want to know how to set it up so that i can apply it to other problems. Heres the problem: The Jones family drove to Disneyland at 50 mph and returned on the same route at 40 mph. Find the distance to Disneyland if the total driving time was 7.2 hours.
I took the formula D=rt and put distance as unknown so the distance to disneyland is equal to 50mph times 3.2 hours(my guess because it would have taken them less time to travel faster) and distance from disneyland is equal to 40mph times 4 hours(guess) [(3.2+4=7.2)hours] Therefore 50x3.2=160 and 40x4=160 I know from logic that the distance in miles from disneyland and to disneyland has to be equal so the answer to the problem has to be 160. But I dont want to guess, so can you help me set up an equation that will get me the same solution??????
Answer by Scriptor(36)   (Show Source):
You can put this solution on YOUR website! Hello,
Call t the time to get there, and T the time to return. Call 2x the total distance (x is the distance to disneyland) Then we have:
50t + 40T = 2x
t + T = 7,2
=> fill in (7,2 - t) for T
50t + 40(7,2 - t) = 2x
Use this together with 50t = x (going to disneyland without returning)
Now you have: 50t + 288 - 40t = 100t
288 = 90t
t = 288/90 = 3.2
=> x = 50*3.2 = 160 ...without guessing ;-)
Greets,
Scriptor
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