SOLUTION: The distance between village A and village B is 6 miles. A person walks part of the way at 5 miles per hour, then jogs the rest of the way at 9 mph. Find a formula that expresses t

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: The distance between village A and village B is 6 miles. A person walks part of the way at 5 miles per hour, then jogs the rest of the way at 9 mph. Find a formula that expresses t      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 334671: The distance between village A and village B is 6 miles. A person walks part of the way at 5 miles per hour, then jogs the rest of the way at 9 mph. Find a formula that expresses the total amount of time for the trip, T, as a function of d, the distance walked.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First I'll write 2 equations: 1 for walking and 1
for jogging:
Walking:
(1) d+=+r%5B1%5D%2At%5B1%5D
If the distance from A to B is 6 mi, then
the distance jogged is 6+-+d mi
Jogging:
(2) 6+-+d+=+r%5B2%5D%2At%5B2%5D
-------------------
given:
r%5B1%5D+=+5 mi/hr
r%5B2%5D+=+9 mi/hr
t%5B1%5D+%2B+t%5B2%5D+=+T hrs
-------------------
I'll rewrite (1) and (2)
(1) d+=+5t%5B1%5D
(2) 6+-+d+=+9t%5B2%5D
Add the equations
6+=+5t%5B1%5D+%2B+9t%5B2%5D
By substitution:
6+=+5t%5B1%5D+%2B+9%2A%28T+-+t%5B1%5D%29
6+=+5t%5B1%5D+%2B+9T+-+9t%5B1%5D
4t%5B1%5D+=+9T+-+6
t%5B1%5D+=+%281%2F4%29%2A%289T+-+6%29
By substitution into (1):
d+=+%285%2F4%29%2A%289T+-+6%29
9T+-+6+=+%284%2F5%29%2Ad
9T+=+%284%2F5%29%2Ad+%2B+6
T+=+%284%2F45%29%2Ad+%2B+2%2F3 hrs answer
check answer:
Suppose d+=+1 mi
(1) d+=+5t%5B1%5D
t%5B1%5D+=+1%2F5
(2) 6+-+d+=+9t%5B2%5D
5+=+9t%5B2%5D
t%5B2%5D+=+5%2F9
T+=+t%5B1%5D+%2B+t%5B2%5D
T+=+1%2F5+%2B+5%2F9
T+=+%289+%2B+25%29%2F45
T+=+34%2F45
From answer:
34%2F45+=+%284%2F45%29%2A1+%2B+2%2F3
34%2F45++=+4%2F45+%2B+30%2F45
34%2F45+=+34%2F45
OK