SOLUTION: not on book Help!! Mandy begins bicycling west a 30 miles per hour at 11 am. If Liz leaves from the same point 20 minute latera bicycling west at 36 miles per hour, when will s

Question 79615: not on book Help!!
Mandy begins bicycling west a 30 miles per hour at 11 am. If Liz leaves from the same point 20 minute latera bicycling west at 36 miles per hour, when will she catch Mandy?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
Mandy begins bicycling west at 30 miles per hour at 11 am. If Liz leaves from
the same point 20 minute latera bicycling west at 36 miles per hour, when will
she catch Mandy?


First I'll show you how to do it in your head. Then I'll show you how
your teacher wants you to work it.

20 minutes is 1/3 of an hour, so since Mandy can go 30 miles in one hour,
she goes 10 miles in that 1/3 of an hour. So she's ahead of Liz by 10 miles
when Liz starts out.  Liz goes 6 mph faster than Mandy, so she can make
up 6 miles of Mandy's 10 mile lead in one hour.  She can make up 2 more
miles of Mandy's lead in 1/3 of an hour, and the remaining 2 miles of Mandy's
lead in another 1/3 of an hour. So it will take her 1 2/3 hours or an hour
and 40 minutes.  Since Liz started at 11:20, she will catch Mandy at 1 PM.

But your teacher will not accept that way, but it is interesting that you
can do it in your head.  But you might mention this to your teacher. Here's
how your teacher wants you to do it:

Let t = the number of hours after 11 AM that Liz 
catches Mandy

Make this chart

         DISTANCE     RATE    TIME
Liz                                
Mandy                                

Mandy travels the entire time, so her time is t,
Fill that in:

         DISTANCE     RATE    TIME
Liz                             
Mandy                           t      

Fill in their rates as 36 and 30 mph

         DISTANCE     RATE    TIME
Liz                    36       
Mandy                  30       t     

Liz's time is 20 minutes less than Mandy's
time.  Since 20 minutes is 1/3 of an hour,
Liz's time is t-1/3, so fill that in as
Liz's time:

         DISTANCE     RATE    TIME
Liz                    36     t-1/3
Mandy                  30       t

Now use DISTANCE = RATE�TIME to fill in
the two distances:

         DISTANCE     RATE    TIME
Liz      36(t-1/3)     36     t-1/3
Mandy       30t        30       t

Now that the chart is filled in we make
our equation by noting that when Liz
catches Mandy they will have traveled
the SAME distance, so set their two
distances equal:

     36(t - 1/3) = 30t

        36t - 12 = 30t 

              6t = 12

               t = 2

2 hours past 11AM is 1PM.  So Liz catches
Mandy at 1PM.

Edwin

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