# Why is my solution wrong?

Discussion in 'Algebra' started by user1234, Aug 18, 2019.

1. ### user1234Guest

I am trying to solve the following algebra question but I don’t understand why my solution is wrong.

Kesha drove from Buffalo to Syracuse at an average rate of 48 miles per hour. On the
return trip along the same road she was able to travel at an average rate of 60 miles per
hour. The trip from Buffalo to Syracuse took one-half hour longer than the return trip. How
long did the return trip take?

Here is my solution.

60x = 48x + 0.5
12x = 0.5
12/0.5 = 24

The correct answer is 2 but how?

user1234, Aug 18, 2019

2. ### Devilman93

Joined:
Dec 17, 2019
Messages:
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0
you solved for the wrong thing

Devilman93, Dec 17, 2019

3. ### MDV

Joined:
Jan 18, 2020
Messages:
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d = distance (Buffalo to Syracuse is same distance as Syracuse to Buffalo!!)
x = time taken

and of course, speed * distance = time;

48 * d = x // Buffalo to Syracuse (1)
60 * d = x + 0.5 // Syracuse to Buffalo

From (1) : d = x /48
Substitute for 'd' in (2): 60 * (x / 48) = x + 0.5
Rearrange: (60/48)x = x + 0.5
( (60/48) - 1 ) x = 0.5
x = 0.5 / (60/48 - 1)
x = 2

MDV, Jan 18, 2020