Solve Slope & Y-Intercept for Cliff Height & Time to Top

[044]

Homework Statement

Hiker 1 was at the bottom of a cliff. He started climbing trying to maintain a constant rate of speed. After 2 minutes he was 160 ft from the bottom of the cliff and after 5 minutes he was 380 ft from the bottom. What is the height of the cliff and when did he reach the top?

Homework Equations

Found slope with m = 380 - 160/5 - 2

y = 73.3x + b or y = 220/3 (x) + b

The Attempt at a Solution

I found y-intercept to be 13.3 ft which as the height of the cliff doesn't make sense to me. I can think of no way to determine how long to the top going up. I can see how you could calculate the height and time going down, but not up.

 

[Mark44]

Homework Statement

Hiker 1 was at the bottom of a cliff. He started climbing trying to maintain a constant rate of speed. After 2 minutes he was 160 ft from the bottom of the cliff and after 5 minutes he was 380 ft from the bottom. What is the height of the cliff and when did he reach the top?

Homework Equations

Found slope with m = 380 - 160/5 - 2

Please use parentheses. What you should write is m = (380 - 160)/(5 - 2).

y = 73.3x + b or y = 220/3 (x) + b

The Attempt at a Solution

I found y-intercept to be 13.3 ft which as the height of the cliff doesn't make sense to me. I can think of no way to determine how long to the top going up. I can see how you could calculate the height and time going down, but not up.

Is this the exact wording of the problem? If so, it doesn't seem to me that you are given enough information to answer the question. All you know is that at 2 minutes he has climbed 160 feet, and after 5 minutes, he has climbed 380 feet.

BTW, this seems to me to be a problem cooked up by someone who has no notion of rock climbing. (If you are climbing a cliff, you are rock-climbing, not hiking.) If the climber could maintain the pace he had in the first two minutes, he would be climbing 80 ft/min., or 4800 ft/hour. I don't think anyone could do this.