Question 260463
This is an RTD problem. Here is a table based on the given information:
brothers . . . . . . . . rate . . . . . . . . . .time . . . . . . . . . .distance
brother . . . . . . . . . .D/40 . . . . . . . .. .T+8 . . . . . . . . . . . .D
me . . . . . . . . . . . . . D/30. . . . . . . . . .T . . . . . . . . . . . . . .D
you want to catch up to brother, so the distances must be equal.
(i) {{{(D/40)*(T+ 8) = (D/30)*T}}}
cross multiply to get
(ii) {{{30*D*(T+8) = 40DT}}}
simplify to get
(iii) {{{30DT + 240D = 40DT}}}
subtracting, we get
 (iv) {{{240D = 10DT}}}
divide by 10D to get
(v) {{{24 = T}}}
You will catch up after 24 minutes.