Question

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 at a rate of 3 mph, so d = 3(t + 7). If she gets to the station 5 minutes early it means the time t can be 5 minutes less at a rate of 4 mph 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. In two or more complete sentences, explain his mistake. Include the correct calculations and solutions in your answer.

Answer 1

d= 3(t + 7) ...............(1)

d= 4(t- 5)...................(2)

3(t + 7) = 4(t - 5)

3t + 21 = 4t - 20

t = 41

For finding the Distance to the station, we need to use either equation (1) or (2). Here two different rates are given 3 mph and 4 mph. So, we can't consider r= 3 only.

If we use the equation (1), then

d= 3(t + 7)

d= 3(41 +7)

d= 3(48) = 144

We can also use the equation (2)

d = 4(t - 5)

d= 4(41- 5)

d= 4(36) = 144

So, the correct distance to the station is 144 miles.