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​+t3​t1​+t2​+5t3​5t1​+t2​+t3​​=4=20=20​
whose solution is t1​=3,t2​=2,t3​=3.
Hence t1​+t2​+t3​=8= total number of hours.