Need help with distance word problem

[chijioke]

$$\text{A motorist travelled from Ibadan to Lagos, a distance of 142 km, at an average speed of 60km/hr.}\\ \text{He spent} ~2\frac{1}{2}~hrs~ \text{in Lagos and then returned to Ibadan at an average speed of 80 km/hr.}$$(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
$$\text{time spent in Lagos}~ = 2\frac{1}{2}~hrs$$average speed for the journey from Ibadan to Lagos = 60km/h
$$\text{time spent for the journey from Ibadan to Lagos}~ =\frac{142}{60}= 2\frac{11}{30}~hrs$$Come to think of it, distance from Ibadan to Lagos =142 km
Speed for journey from Lagos to Ibadan = 80km/hr
$$\text{then time spent on the road travelling back to Ibadan} = \frac{142}{80}=1\frac{31}{40~hrs}$$$$\text{since he spent}~1\frac{31}{40}~hrs \text{on the road}$$$$\text{He arrived at Ibadan}~1\frac{31}{40} +2\frac{1}{2}~hrs~= 4\frac{11}{40}~hrs$$Am I right?

 

[khansaheb]

$$\text{A motorist travelled from Ibadan to Lagos, a distance of 142 km, at an average speed of 60km/hr.}\\ \text{He spent} ~2\frac{1}{2}~hrs~ \text{in Lagos and then returned to Ibadan at an average speed of 80 km/hr.}$$(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
$$\text{time spent in Lagos}~ = 2\frac{1}{2}~hrs$$average speed for the journey from Ibadan to Lagos = 60km/h
$$\text{time spent for the journey from Ibadan to Lagos}~ =\frac{142}{60}= 2\frac{11}{30}~hrs$$Come to think of it, distance from Ibadan to Lagos =142 km
Speed for journey from Lagos to Ibadan = 80km/hr
$$\text{then time spent on the road travelling back to Ibadan} = \frac{142}{80}=1\frac{31}{40~hrs}$$$$\text{since he spent}~1\frac{31}{40}~hrs \text{on the road}$$$$\text{He arrived at Ibadan}~1\frac{31}{40} +2\frac{1}{2}~hrs~= 4\frac{11}{40}~hrs$$Am I right?

You have posted an incomplete problem - it is missing the starting time!
Post the exact problem as it was presented to you.

 

[chijioke]

You have posted an incomplete problem - it is missing the starting time!
Post the exact problem as it was presented to you.

Attached is the exact problem.

 

[Cubist]

You can't answer the question as written. I suspect that they intended to write:-

(i) After how much time did the man arrive back in Ibadan?

...and this can be answered.

Am I right?

Your answer is unfortunately wrong... you didn't use the following part of your calculation in your final answer...

$$\text{time spent for the journey from Ibadan to Lagos}~ =\frac{142}{60}= 2\frac{11}{30}~hrs$$

 

[chijioke]

You can't answer the question as written. I suspect that they intended to write:-

(i) After how much time did the man arrive back in Ibadan?

...and this can be answered.


Your answer is unfortunately wrong... you didn't use the following part of your calculation in your final answer...

If they intend to ask of the total time spent by the man then this is the answer =
$$1\frac{31}{40}+2\frac{1}{2}+2\frac{11}{30}=6\frac{77}{120}~hrs$$Isn't it?

 

[chijioke]

For number (ii)
Average speed $$= \frac{\text{total distance for the journey tro and fro}}{\text{total spent}} \\ = \frac{142+142}{2\frac{11}{30}+1\frac{31}{40}} = \frac{284}{4\frac{17}{120}} \\=68\frac{4}{7}~km/hr$$

 

[Cubist]

If they intend to ask of the total time spent by the man then this is the answer =
$$1\frac{31}{40}+2\frac{1}{2}+2\frac{11}{30}=6\frac{77}{120}~hrs$$Isn't it?

Yes

For number (ii)
Average speed $$= \frac{\text{total distance for the journey tro and fro}}{\text{total spent}} \\ = \frac{142+142}{2\frac{11}{30}+1\frac{31}{40}} = \frac{284}{4\frac{17}{120}} \\=68\frac{4}{7}~km/hr$$

This is correct if they want the average speed for all the time that was spent on the move.
But, in my opinion, it's also possible that they might want the average speed over the whole 6 77/120 hours.
This question isn't well written.

 

[chijioke]

W

But, in my opinion, it's also possible that they might want the average speed over the whole 6 77/120 hours.

Why do you suggest 677/120 hours?

 

[khansaheb]

W

Why do you suggest 677/120 hours?

If notice carefully, there is a (space) between 6 & 77. intended writing was $\displaystyle 6\frac{77}{120}$