Question

A bus covered 400km distance between points A and B at a certain speed. On the return trip, the biker traveled at the same speed for 2 hours and then increased the speed by 10km an hour until it reached A, this spending 20 fewer minutes on the return treip. How long did the return trip take?

Answer 1

you need to start building your own equations describing what is happening. just distance = speed * time stuff, but building in the subtleties of this situation.

for example you might start by letting v = the speed on the outward leg. therefore you already have the equation 400 = v * T1 where T1 is the duration of the outward leg. If the total duration of the return leg is T2, you also have T2 = T1 - 1/3 (the 1/3 being the third of an hour you saved by going faster.

You also know that if the final part at the higher speed is called t, then 400 = 2 * v + t *( v + 10). that's 2 hours at speed v, then travelling at 10 + v for the last period of time t.

this is all you need to solve this - plus of course cranking through the equations and solving.

there may be other ways of building the basic equations. just give it a go, either the way i suggest or using your own formula.

just be sure to keep the units consistent. my formula work in kilometres, hours and km/hr.