[basilrazi]

A train leaves from Newcastle for Sydney at 7$5a, while another train leaves from Sydney to Newcastle at 8:15am. The first train arrives in Sydney 40 minutes after the trains pass, while the train to Newcastle arrives 1 hour 40 minutes after they pass. Assuming that the trains travel at different but constant speeds find the times the two trains passed each other.

Please answer this for me. Thanks

[basilrazi]

Sorry this is what it should be:

A train leaves from Newcastle for Sydney at 7:45am, while another train leaves from Sydney to Newcastle at 8:15am. The first train arrives in Sydney 40 minutes after the trains pass, while the train to Newcastle arrives 1 hour 40 minutes after they pass. Assuming that the trains travel at different but constant speeds. Find the time the two trains passed each other.

[ebaines]

I suggest you set up an equation that equates the time the two trains meet. Call the two trains A and B, the distance from Newcastle to the meet point D_a and the distance from Sydney to the meet point D_b The time it takes for train A to get to the meet point from Newcastle is D_a/R_a, and the time for train B to get there from Sydney is D_b/R_b. Since they get there at the same time, you have:

7:45 + D_a/R_a= 8:15 + D_b/R_b

You also know that D_a = 100/60 * R_b, and D_b = 40/60*R_a

Put these together to eliminate the D_a and D-b terms, and you will get an equation in terms of R_a/R_b, which you can solve. Once you have the ratio of R_a/R_b, you can determine the time it takes for train B to go from Sydney to the meet point based on

D_b = R_a*40 min = R_b * Time_b, or Time_b = R_a/R_b* 40 min.

From this you can determine the meet time.