Calculating Distance and Speed: Solving a Robert Service Question

[richezzy]

Homework Statement

Robert Service race down the frozen Mackenzie river to rendezvous with Sam McGee who lay dying in a camp. He had a team of five huskies pulling his sled at full speed for 24 hours, then 2 dogs ran off. The trip continued at 3/5 the original speed
and he reached his goal 48 hours later than he would have had the full speed been maintained. If the the two fickle dogs had stayed on the job for an additional 50km, he would arrive 24 hours late instead. What distance did the trip cover?

Homework Equations

d= vt

The Attempt at a Solution

I believed the first equation was
d = (v x 24) + (3/5v x 48) and d+50 = v x 24, isolated the two d and solved for the original speed, however my teacher told me I was way off. I am not quite sure of how to approach this question, and any help would be greatly appreciated.

 

[zooxanthellae]

The key seems to be the last bit of information. If the 2 dogs had stayed for 50 more km then he would have been 24 hours late, not 48. So those 2 dogs contributed a difference of 24 hours. How can you use that?

 

[HallsofIvy]

Yes. Your equation has two unknowns, d and v. To solve for v, you need to know d and to get that you need to use the last bit of information, that you did not use, to get a second equation.

 

[justinh8]

I got the same question,
so in the final part he would travel 50km in 24 hours
and he would have also traveled 50km in 24 hours with 3 dogs
and in the first 24 hours it would be 50/3 x 5 = 83.3333
so total distance would equal 50 + 50 + 83.333 = 183.333km?
cheya richezzzyy

 

[analyzer]

Actually, I set a system of five equations with five unknowns. The unknowns are distance traveled, speed with five dogs, remaining time employed (i.e. apart from the 24 hours) had the full speed been maintained, remaining time employed with three dogs in the first situation, and remaining time employed with three dogs in the latter case. The answer is not 183.333 km.

 

[RichardT]

I have the possible answers for this question from my teacher:100, 133, 167, 200, or 267 (all kilometers)

 

[verty]

Good question this, you need to write everything clearly and continue even when it looks impossible. Calculate everything you can and you'll get there.