SOLUTION: Tim leaves on his bike at 10 a.m. traveling 16 mph. At 10:29 a.m. his sister noticed he forgot his wallet. She leaves on the same road at 10:30 a.m. driving 36 mph. After how ma

Algebra ->  Test -> SOLUTION: Tim leaves on his bike at 10 a.m. traveling 16 mph. At 10:29 a.m. his sister noticed he forgot his wallet. She leaves on the same road at 10:30 a.m. driving 36 mph. After how ma      Log On


   



Question 543628: Tim leaves on his bike at 10 a.m. traveling 16 mph. At 10:29 a.m. his sister noticed he forgot his wallet. She leaves on the same road at 10:30 a.m. driving 36 mph. After how many minutes will she reach him
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
How much of a head start did Tim have?
10 AM to 10:30 AM is +.5+ hrs
At +16+ mi/hr, Tim goes
+d%5B1%5D+=+16%2A.5+
+d%5B1%5D+=+8+ mi
--------------
Let t = the time it takes for his sister
to catch him.
Let d = the distance she has to travel
Her equation:
(1) +d+=+36t+
Tim's equation:
(2) +d+-+8+=+16t+
Note that they will both trvel for the same
amount of time after Sister leaves and Tim
has 8 miles less to travel.
Substitute (1) into (2)
(2) +36t+-+8+=+16t+
(2) +20t+=+8+
(2) +t+=+.4+ hrs
+.4%2A60+=+24+ min
After 24 minutes she will catch him