Hey,

Could someone please explain how this can be solved using the backsolving technique, I’m hitting a dead end. Even the algebraic approach would be a savior actually.

Thank you!

Hey,

Could someone please explain how this can be solved using the backsolving technique, I’m hitting a dead end. Even the algebraic approach would be a savior actually.

Thank you!

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I am not sure how to solve this via backsolving

The first thing I will do is, why make Tom run in the opposite direction the direction doesn’t matter

By simply changing that, the question becomes

The time difference b/w the point where Tom overtakes Linda and the time where Tom is ahead of Linda by the exact distance Linda has covered

Now, let the time taken by Linda to reach the point of overtaking be ‘t’ (hours)

In ‘t’ time L has covered 2t miles

Distance travelled by T to overtake her is also 2t

Time taken by Tom to reach that point = t-1 (because he started 1 hour late), but also, 2t/6 hours (distance/ speed)

t -1 = 2t/6

6t - 6 = 2t

4t = 6

t = 1.5 hours

This is now a new starting point, let’s say B

For any new time “t*”, the new distance travelled by Linda = 2t* and the new distance travelled by Tom = 6t*

Total distance travelled by Linda = 2t + 2t*

Total distance travelled by Tom = 2t + 6t*

According to the question:

2t + 6t* = 2(2t + 2t*)

2t + 6t* = 4t + 4t*

2t* = 2t

t* = t = 1.5hours = 90 minutes (the ans)

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Thank you, this is super helpful!!