Question 1194484
A driver traveled from A to B. On the return trip, he averaged 10kph more and that trip took 30 minutes less. If he had averaged 10 kph less on the outgoing trip, that trip would have taken 40 minutes more. On the trip from A to B what was the average speed
<pre>Let outgoing speed and time be S and T, respectively
Then distance from A to B, or B to A = ST

Since the return trip took 30 minutes ({{{1/2}}} hour) less when traveling 10 km/h more, then the
return speed and return time are, {{{matrix(1,3, "S + 10,", and, T - 1/2)}}}, respectively
We then get the following DISTANCE equation: {{{system(matrix(2,3, ST, "=", (S + 10)(T - 1/2), ST, "=", ST - (S/2) + 10T - 5), matrix(1,6, 10T - (S/2), "=", 5, "--------", eq, "(i)"))}}}

Since the outgoing trip would've taken 40 minutes ({{{matrix(1,3, 40/60, or, 2/3)}}} hour) more when traveling 10 km/h less, then the
return speed and return time would've been, {{{matrix(1,3, "S - 10,", and, T + 2/3)}}}, respectively
We then get the following DISTANCE equation: {{{system(matrix(2,3, ST, "=", (S - 10)(T + 2/3), ST, "=", ST + (2S/3) - 10T - 20/3), matrix(1,6, - 10T + 2S/3, "=", 20/3, "--------", eq, "(ii)"))}}}

                                                         {{{matrix(1,3, 2S/3 - S/2, "=", 20/3 + 5)}}} ------- Adding eqs (ii) & (i)
                                                         4S - 3S = 40 + 30 ----- Multiplying by LCD, 6 
                                           Outgoing speed, or {{{highlight_green(matrix(1,4, S, "=", 70, "km/h"))}}}</pre>