Help - algebraic problem?

Question

Two students, Alex and Boris, went out of two places which are 920 km apart, towards each other. Alex went out at 8:00am and Boris at 10:00am. They met at 15:00. Alex was faster by 8 km/h than Boris. Find their constant speeds.

And could you explain the working out?

Answer 1

Step 1: Set this up by defining equations for the distances traveled as a (for Alex) and b (for Boris), the times, and the speeds:
a + b = 920 (from the first sentence)
ta = Alex's time = 15 - 8 = 7 hours (2nd and third sentence)
tb = Boris' time = 15 - 10 = 5 hours
va = Alex's velocity = vb + 8 (last sentence)

va = a / ta (velocity = distance / time)
vb = b / tb

Step 2: Find b in terms of a.
a + b = 920
b = 920 - a

Step 3: Take the velocity equation for va and vb, substitute with the definition of b in terms of a, and solve.
va = vb + 8
a/ta = b/tb + 8
a/7 = b/5 + 8
a/7 = (920 - a)/5 + 8 (substitute for b)
a/7 = 184 - a/5 + 8
a/7 + a/5 = 192
(a/7 + a/5) * 35 = 192 * 35
5a + 7a = 6720
12a = 6720
a = 560 mi

Step 4: Use a to find b:
a + b = 920
560 + b = 920
b = 360

Step 5: Use a and b and the times to find the speeds:
va = a/ta = 560 / 7 = 80 km/h
vb = b/tb = 360 / 5 = 72 km/h