Let the distance between A and B be ‘x’ miles.
Let their speeds be T, J and B in miles/hour
When Tom meets Jerry:
Distance travelled by Tom = x + 9
Distance travelled by Jerry = x – 9
Time taken will be the same => =
Or = -- (1)
When Jerry meets Bill:
Distance travelled by Jerry = x + 7
Distance travelled by Bill = x – 7
Time taken will be the same => =
Or = -- (2)
Given 3T = 5B
or =
From (1) and (2)
= *
= *
5(x - 9)(x - 7) = 3 (x + 9) (x + 7)
5x^{2} – 80x + 315 = 3x^{2} + 48x + 189
2x^{2} – 128x + 126 = 0
x^{2} – 64x + 63 = 0
x = 63 or x = 1
X has to be 63
Correct Answer: Distance is 63 miles