What was the average speed of the herd for the part beyond Forde Lake in the following question:Several cows from the Qamanirjuaq Caribou Herd took 4 days longer to travel 70km to Forde Lake,...

What was the average speed of the herd for the part beyond Forde Lake in the following question:

Several cows from the Qamanirjuaq Caribou Herd took 4 days longer to travel 70km to Forde Lake, Nunavut, than it took them to travel 60 km north beyond Forde Lake. They averaged 5 km/h less before Forde Lake because foraging was better. What was their average speed for the part beyond Forde Lake? Round your answer to the nearest tenth of a kilometer per hour.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The cows traveled 70 km to Forde Lake and then another 60 km beyond Forde Lake. The speed during the first 70 km was 5 km/h less than that for the rest of the 60 km. The time taken to travel the first 70 km is 4 days more than that for the rest of the distance.

Let the speed of the herd beyond Forde Lake be r, the speed before Forde Lake is r - 5.

The distance of 70 km is traveled in `70/(r - 5)` hours and the 60 km is traveled in `60/r` hours.

It is given that the herd takes 4 days or 96 hours more to travel the first 70 km than the rest of the 60 km.

=> `70/(r-5)+96 = 60/r`

=> 70r + 96(r - 5)r = 60(r-5)

=> 70r + 96r^2 - 480r = 60r - 300

=> 96r^2 - 478r + 300 = 0

Solving for r,

r1 = `(478+sqrt(478^2 - 96*300*4))/192 = ` 4.242

and r2 = `(478-sqrt(478^2-4*96*300))/192` =0.736

In both the cases, the speed of the herd would have to be negative while traveling to Forde lake which is not possible. The given information does not yield a consistent answer.

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