Question 1101384
a) i) After travelling for {{{2.5hours}}} ,
the bus had covered a distance of
{{{("60 km / hr .")(2.5hours)=150km}}} ,
so the distance of the bus from Nairobi when the car took off was {{{highlight(150km)}}} .
 
ii) The car was moving at a speed
{{{"100 km / hr ."-"60 km / hr ."="40 km / hr ."}}} faster than the bus,
so it was shortening the distance between them at that rate.
It would have taken {{{150km/"40 km / hr ."=3.75 hours}}} to catch up with the bus.
During that time, the car would travel
{{{("100 km / hr .")(3.75hours)=375km}}} ,
so the distance the car travelled to catch up with the bus was
{{{highlight(375km)}}} .
 
b) At the time the car caught up with the bus,
they both were {{{500km-375km=125km}}} away from Nairobi.
It would take the bus another {{{125km/"60 km / hr ."=125/60}}}{{{hours}}} to get to Nairobi.
That is {{{125minutes}}} or {{{2&5/60}}}hours or 2 hours and 5 minutes.
As the car stopped for 25 minutes, to get to Nairobi at the same time as the bus,
it would have to travel the remaining 125 km in
125 minutes - 25 minutes = 100 minutes.
That is {{{100/60}}}{{{hours=5/3}}}{{{hours}}} .
For that to happen, its average speed, in km/hr. would have to be
{{{125/"5 / 3"=125(3/5)=75}}} .
The new average speed at which the car travelled in order to reach Nairobi at the same time as the bus was {{{highlight("75 km / hr .")}}} .