Can someone help me with this question please?

Esther drove to work in the morning at an average speed of 45mph. She returned home
In the evening along the same route and averaged 30mph. If esther spent a total of one hour commute to and from work, how many miles did esther drive to work in the morning?

Answer is 18 How do we get that?

distance = speed * time

you know distance was the same in each and that the sum of the times is 1 hour

these are the equations that you initially know:

d = 45 * t_{morn} \\
d = 30 * t_{eve} \\
t_{morn} + t_{eve} = 1 \\


since the first two both equal d you can set them equal to each other:

45 * t_{morn} = 30 * t_{eve}
[math]

now we can solve for one t and substitute into the third equation and solve for the other

[math]
t_{morn} = \frac 2 3 * t_{eve}\\
\frac 2 3 * t_{eve} + t_{eve} = 1 \\
t_{eve} = \frac 3 5


now we can substitute into the 2nd equation to solve for d


d = 30 * \frac 3 5 \\
d = 18


Let me know if you have any questions.

Thanks for your help



distance = speed * time

you know distance was the same in each and that the sum of the times is 1 hour

these are the equations that you initially know:

d = 45 * t_{morn} \\
d = 30 * t_{eve} \\
t_{morn} + t_{eve} = 1 \\


since the first two both equal d you can set them equal to each other:

45 * t_{morn} = 30 * t_{eve}
[math]

now we can solve for one t and substitute into the third equation and solve for the other

[math]
t_{morn} = \frac 2 3 * t_{eve}\\
\frac 2 3 * t_{eve} + t_{eve} = 1 \\
t_{eve} = \frac 3 5


now we can substitute into the 2nd equation to solve for d


d = 30 * \frac 3 5 \\
d = 18


Let me know if you have any questions.