Problem: Tom, Dick and Harry started out on a 100-mile journey. Tom and Harry went by automobile at the rate of 25 mph , while Dick walked at the rate of 5 mph. After a certain distance, Tom let Harry off, who walked on at 5 mph, while Tom went back for Dick and got him to the destination at the same time that Harry arrived. The number of hours required for the trip was:
Answer Choices:
A. 5
B. 6
C. 7
D. 8
E. none of these answers
Solution:
Let t1,t2,t3 be the number of hours, respectively, that the car travels forward, back to pick up Dick, then forward to the destination. Then we may write
25⋅t1−25⋅t2+25⋅t3=1005⋅t1+5⋅t2+25⋅t3=10025⋅t1+5⋅t2+5⋅t3=100 for car for Dick for Harry
This system of simultaneous equations is equivalent to the system
t1−t2+t3t1+t2+5t35t1+t2+t3=4=20=20
whose solution is t1=3,t2=2,t3=3.
Hence t1+t2+t3=8= total number of hours.