SOLUTION: ****Corrected the complete question***** Gilda walks to the train station. If she walks at the rate of 3 mph, she misses her train by 7 minutes. However, if she walks at the rat

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: ****Corrected the complete question***** Gilda walks to the train station. If she walks at the rate of 3 mph, she misses her train by 7 minutes. However, if she walks at the rat      Log On


   



Question 1029838: ****Corrected the complete question*****
Gilda walks to the train station. If she walks at the rate of 3 mph, she misses her train by 7 minutes. However, if she walks at the rate of 4 mph, she reaches the station 5 minutes before the arrival of the train. Find the distance Gilda walks to the station.
David knew he made a mistake when he calculated that Gilda walks 123 miles to the station. Read through David's calculations:
Using d = rt, the distance is the same, but the rate and time are different.
If Gilda misses the train, it means the time t needs 7 more minutes so d = 3(t + 7).
If she gets to the station 5 minutes early means the time t can be 5 minutes less so d = 4(t - 5).
3(t + 7) = 4(t - 5)
3t + 21 = 4t - 20
t = 41
d = rt, so d = 3(41) = 123
Find David's mistake in his calculations. Include the correct calculations and solutions.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Two mistakes.
Time is measured in minutes.
Rate is measured in miles/hour.
You must convert one of them to be consistent.
3%28mile%2Fhr%29%2A%281%2F60%29%28hr%2Fmin%29=%281%2F20%29%28mile%2Fmin%29
4%28mile%2Fhr%29%2A%281%2F60%29%28hr%2Fmin%29=%281%2F15%29%28mile%2Fmin%29
%281%2F20%29%28t%2B7%29=%281%2F15%29%28t-5%29
t=41min
Answer is the same but the units are now correct.
When you measured distance, you have to use either of the formulas,
d=%281%2F20%29%28t%2B7%29
d=%281%2F15%29%28t-5%29
If you use d=3t, you'll get the wrong answer since d=3t and d=4t would give you different answers.
d=%281%2F20%29%2848%29=48%2F20=2.4miles
d=%281%2F15%29%2836%29=2.4miles