Time speed distance

[dwars]

If I am assuming distance to be constant Speed(a)/Speed(b) = 5/6
Now Time(a) /Time(b) = 6/5
Reducing the gap of half an hour, we get
Time(a) / Time(b) = 3/ 2.5
So, A & B will cross each other at 3 PM because A departs at 12 pm & B at 12:30 PM.
However, the answer is 2:30 PM.
I am not able to get where am I going wrong.

 

[Dr.Peterson]

View attachment 21130

If I am assuming distance to be constant Speed(a)/Speed(b) = 5/6
Now Time(a) /Time(b) = 6/5
Reducing the gap of half an hour, we get
Time(a) / Time(b) = 3/ 2.5
So, A & B will cross each other at 3 PM because A departs at 12 pm & B at 12:30 PM.
However, the answer is 2:30 PM.
I am not able to get where am I going wrong.

Well, first we can check their answer to see if they are right.

At 2:30, A has been going for 2.5 hr at 50 mph, for a distance of 125 miles; B has been going for 2 hr at 60 mph, for a distance of 120 miles.

They are not in the same place, so the answer you were given is wrong.

You can do the same check on your own answer.

I suspect that someone solved it using algebra and didn't check what their variable meant, taking 2.5 hr to be A's time instead of B's.

Don't always assume that the given answer is correct. Others besides you are human ...

 

[HallsofIvy]

At 50 mph, t hours after 12:00, train A will have gone 50t miles. At 60mph, t- 1/2 hours after 12:30, train B will have gone 60(t- 1/2)= 60t- 30 miles. If they meet at time t, the total distance A and B have gone is the 245 miles. 50t+ 60t- 30= 110t- 30= 245. Adding 30 to both sides 110t= 275. t= 275/110= 2.5. Since t is the number of hours since noon, the two trains meet at 2:30 P.M. NOT 3:00 P.M.

Check: at 50 mph, train A has gone 2.5*50= 125 miles at 2:30 P.M. and train B, at 60 mph for 2 hours will have gone 120 miles. The total distance traveled is 225+ 120= 245 miles.

 

[Steven G]

Well, first we can check their answer to see if they are right.

At 2:30, A has been going for 2.5 hr at 50 mph, for a distance of 125 miles; B has been going for 2 hr at 60 mph, for a distance of 120 miles.

They are not in the same place, so the answer you were given is wrong.

You can do the same check on your own answer.

I suspect that someone solved it using algebra and didn't check what their variable meant, taking 2.5 hr to be A's time instead of B's.

Don't always assume that the given answer is correct. Others besides you are human ...

Oops, the two trains do not have to travel the same distance to meet. As I am sure you know, they have to travel a sum of 245 miles to meet.

 

[Dr.Peterson]

Yup, I didn't read carefully that they go in opposite directions, and took it as an overtaking problem -- in part because the OP seemed to take it that way, and I followed.

I've never been in the corner. Where do I find it?