Two hikers are miles apart and walking toward each other. They meet in 10 hours. Find the rate of each hiker if one hiker walks 1.1 mph faster than the other.

Question

Two hikers are miles apart and walking toward each other. They meet in 10 hours. Find the rate of each hiker if one hiker walks 1.1 mph faster than the other.

Answer 1

If one walked at near zero speed and the other at 1.1 mph, they would cover in 10 hours 11 miles.

If one walked at 1 mph the other at 2.1 mph, they would cover 31 miles in 10 hours

Without knowing the distance covered, there doesn't seem to be any solution to their respective speeds

d=rt distance = rate of speed times time

the slower hiker goes x miles. the faster goes d-x miles, the total distance minus what the slower hiker covers.

speed for the slower is r, for the faster r+1.1

time is the same for both, 10 hours

for the slower 10r=x for the faster hiker 10(r+1.1)=10r + 11 = d-x

that's 2 equations 3 unknowns. to solve it we need to know d the distance travelled, how far apart were they at the start of 10 hours?

10r+11 = d-x

10r = x

subtract to get

11 = d-2x

2x = 11-d

x = 5.5 - d/2 = distance of the slower hiker

10r = x = 5.5-d/2

r = 5.5/10 - d/20 = speed of the slower hiker

r+1.1 = 16.5/10 - d/20 = speed of the faster hiker. Just plug in the distance d to get a unique solution

Answer 2

Evelyn

I will model for you, using 8 and 1.5.

Suppose they are m miles apart when they start (you must know m), and assume the speed of the slower hiker is h miles per hour..

Then after 8 hours.

Lets say the slower hiker goes west - east, and the faster one east - west.

After 8 hours. Slower hiker has gone 8 h miles

Faster one has gone 8 (h + 1.5)

As they meet m - 8h = 8 (h + 1.5)

So if you know m. Change this equation so it fits your numbers, then solve for h.

Mike