[math]\text{A motorist travelled from Ibadan to Lagos, a distance of 142 km, at an average speed of 60km/hr.}\\
\text{He spent} ~2\frac{1}{2}~hrs~ \text{in Lagos and then returned to Ibadan at an average speed of 80 km/hr.}[/math](i) At what time did the man arrive back in Ibadan?
(ii) Find his average speed for the total journey.
SOLUTION
(i) distance from Ibadan to Lagos, d= 142km
[math]\text{time spent in Lagos}~ = 2\frac{1}{2}~hrs[/math]average speed for the journey from Ibadan to Lagos = 60km/h
[math]\text{time spent for the journey from Ibadan to Lagos}~ =\frac{142}{60}= 2\frac{11}{30}~hrs[/math]Come to think of it, distance from Ibadan to Lagos =142 km
Speed for journey from Lagos to Ibadan = 80km/hr
[math]\text{then time spent on the road travelling back to Ibadan} = \frac{142}{80}=1\frac{31}{40~hrs}[/math][math]\text{since he spent}~1\frac{31}{40}~hrs \text{on the road}[/math][math]\text{He arrived at Ibadan}~1\frac{31}{40} +2\frac{1}{2}~hrs~= 4\frac{11}{40}~hrs[/math]Am I right?
(ii) Find his average speed for the total journey.
SOLUTION
(i) distance from Ibadan to Lagos, d= 142km
[math]\text{time spent in Lagos}~ = 2\frac{1}{2}~hrs[/math]average speed for the journey from Ibadan to Lagos = 60km/h
[math]\text{time spent for the journey from Ibadan to Lagos}~ =\frac{142}{60}= 2\frac{11}{30}~hrs[/math]Come to think of it, distance from Ibadan to Lagos =142 km
Speed for journey from Lagos to Ibadan = 80km/hr
[math]\text{then time spent on the road travelling back to Ibadan} = \frac{142}{80}=1\frac{31}{40~hrs}[/math][math]\text{since he spent}~1\frac{31}{40}~hrs \text{on the road}[/math][math]\text{He arrived at Ibadan}~1\frac{31}{40} +2\frac{1}{2}~hrs~= 4\frac{11}{40}~hrs[/math]Am I right?