How long will it take for hikers to meet

Question

Benny and Anna are 13 miles apart hiking toward each other. How long will it take them to meet if Benny walks at 3 miles per hour and Anna walks 1 mph faster?

Answer 1

Let

r_B = the rate of Benny = 3 mph

r_A = the rate of Anna = 4 mph

d = distance covered by Benny when they meet.

13-d = distance covered by Anna when they meet.

t = ? = time when they meet.

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The formula is d = rt.

The value of t in terms of d and r is:

t=d/r

*We are going to use t=d/r because the time consumed by Benny and Anna are the same when they meet somewhere in the middle of 13 miles.

Time of Benny = d/r_B = d/3

Time of Anna = (13-d)/r_A = (13-d)/4

Since the time is the same, put them equal to each other to have an equation:

d/3 = (13-d)/ 4

4d = 3(13-d)

4d = 39 - 3d

7d = 39

d = 39/7 ≈ 5.57 miles

Then solve for the time:

t = d/r = (39/7)/3

t = (39/7)*(1/3)

t = 13/7 ≈ 1.86 hours.

Answer 2

First, if Anna walks 1 mph faster, then Anna is walking 3+1 = 4mph.

Now, we can create an equation to get our answer. Let's say that they each walk h total hours to meet.

By our formula distance = rate * speed, Anna walks 4h miles, and Benny walks 3h miles. We want the total amount of miles they walk to add to 13, because otherwise they would keep walking and miss each other. This gives:

4h + 3h = 13

7h = 13

h = 13/7 hours