Question

Joe Fleet can jog at the rate of 8 mph. Ron Pack can hike carrying camping equipment at the rate of 4 mph. They leave from opposite ends of a 44-mile trail at the same time. How far does Ron travel if he has 15 minutes to set up camp before Joe arrives?

a. 3 1/2 miles
b. 14 miles
c. 25 1/3 miles

Answer 1

Optipn 'c' is correct

Explanation:

We use distance formuls Distance=Speed x Time here;

Let Ron Pack covers distance 'x' and Joe Fleet covers distance 'y' to reach the camp respectively;

Then total distance;

x+y=44 ---------------(1)

Let Joe Fleet reaches camp in time 't'.

Then distance covered by Joe Fleet can be calculated by putting values

Distance=y

Time=t

Speed = 8 mph

==> y=8t-----(2)

Since speed of Ron pack is 4 miles per hour and it reaches 15 minutes earlier than Joe Fleet - so, data for Ron Pack is

Distance=x

Time =t-15 (since Ron takes 15 minutes less than Joe)

v=4mph

Put these values in distance formula;

==> x= 4 (t-15) ----------(3)

Adding eq 2 & 3 we get

x+y = 8t+4(t-15) --------------(4)

from eqs 1 and 4 we can say;

8t+4(t-15) =44

==> 12t-60=44

==>12t=104

==> t = 8.7 minutes-------(5)

Put this value of t in eq 3

x= 4(8.7-15) =25.2 miles