+0  
 
+1
51
2
avatar

Jennifer rode her bike at 12 miles per hour for 4 hours, then put her bike down and began walking at 2 miles per hour. Thomas started walking at 4 miles per hour along the same path at the same time that Jennifer started biking. When he reached the bike, he began riding it at 12 miles per hour. How many hours will it have been since they started when Thomas catches up to Jennifer?

 Jan 24, 2021
 #1
avatar+116126 
+1

Let the time Jennifer walks =  J

4 hrs * 12mph   = 48 miles

The total distance  she travels =  48 + 2J

So  the total hrs  she travels =  4 + J

 

The time it took   Thomas to reach the bike  is     48/ 4   = 12 hours

Let his time on the  bike =  T

So  the   distance  he travels  is    48 +  12T

And the  time he travels =  12 + T

 

The time they  travel is equal    and  so is the  distance  ....so...

 

4 + J  =  12  + T          (1)

48 + 12T  =  48 + 2J      ⇒     12 T  = 2J    ⇒   6T   = J      (2)

 

Sub (2)  into (1)

 

4 + 6T =   12 + T

5T  = 8

T  =  8/5   =   1. 6 hrs

 

The total time to catch  up to Jennofer  =      12 + 1.6  =  13.6  hrs

 

Check

Distance  Jennifer travels =   48 + J  =   48 + 2*6(1.6)  = 67.2 miles

Distance  Thomas  travels  =  48 + 12 (1.6)  =   67.2 miles

 

 

cool cool cool

 Jan 24, 2021
 #2
avatar
0

Jennifer has biked 12 * 4 = 48 miles   while Thomas has walked 4 x 4 = 16 miles

   it will take him 8 more hours to get to the bike  at which time Jennifer will have walked  8 x 2= 16miles

their closing speed once T starts biking is  12 -2 = 10 m/hr       16miles will take   1.6 more hours

4 hours + 8 hours + 1.6 hours =13.6 hours from their start they will meet .

 Jan 24, 2021

63 Online Users

avatar
avatar
avatar
avatar