SOLUTION: Tina is going for a walk, traveling at 4 mph. After 30 minutes, David leaves on his bike to try to catch up; he is traveling at 13 mph. If he follows the same route, how long will

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Tina is going for a walk, traveling at 4 mph. After 30 minutes, David leaves on his bike to try to catch up; he is traveling at 13 mph. If he follows the same route, how long will       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 640276: Tina is going for a walk, traveling at 4 mph. After 30 minutes, David leaves on his bike to try to catch up; he is traveling at 13 mph. If he follows the same route, how long will it take him to catch up (in minutes)? How far will they both have traveled?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Tina's head start is +4%2A.5+=+2+ mi
Start a stopwatch when David leaves
They will both travel for the same amount
of time = t in hours
Let +d+ = distance David travels in miles
----------------------------
Tina's equation:
(1) +d+-+2+=+4t+
David's equation:
(2) +d+=+13t+
-------------
Substitute (2) into (1)
(1) +13t+-+2+=+4t+
(1) +9t+=+2+
(1) +t+=+2%2F9+
Convert to minutes and seconds
+%282%2F9%29%2A60+=+40%2F3+
+40%2F3+=+13+%2B+1%2F3+
+%281%2F3%29%2A60+=+20+
David catches up in 13 min 20 sec
--------------------------
(2) +d+=+13%2A%282%2F9%29+
(2) +d+=+26%2F9+
(2) +d+=+2.889+
+d+-+2+=+.889+
David travels 2.889 mi
Tina also travels 2.889 mi in +30+%2B+13+ min and +20+ sec
---------------------
check:
(1) +d+-+2+=+4t+
(1) +26%2F9+-+2+=+4%2A%282%2F9%29+
(1) +26+-+18+=+8+
(1) +26+=+26+
OK