DISTANCE PROBLEM MPH

Question

CYCLIST STARTS AT A CERTAIN POINT AND RIDES AT A RATE OF 10MPH. TWELVE MINUTES LATER , ANOTHER CYLIST STARTS FROM THE SAME POINT IN THE SAME DIRECTION AND RIDES AT 16MPH. hOW LONG WILL IT TAKE FOR THE SECOND CYCLIST TO CATCH UP WITH THE FIRST?

Answer 1

Hi Again Amie;

I enjoy these questions...

Keep these coming...

Cyclist A...10 m/h, time x

Cyclist B...16 m/h, time (x-12 minutes)

 

The first thing we must notice is that 12 is in minutes, whereas everything else is in hours.

Cyclist B...16 m/h(x-0.2 hours)

 

(10 m/h)(x)=(16 m/h)(x-0.2)

Let's cancel units.  m/h is in the denominator on both sides...

(10 m/h)(x)=(16 m/h)(x-0.2)

10x=16(x-0.2)

10x=16x-3.2

Let's subtract 16x from both sides...

-16x+10x=16x-3.2-16x

-6x=-3.2

Let's divide both sides by -6...

(-6x)/(-6)=(-3.2)/(-6)

x=0.53 hours

x=(0.53 hours)(60 minutes)/(1 hour)]

x=32 minutes

 

32 minutes-12 minutes=20 minutes required for the 2nd cyclist to catch-up with the 1st.

 

Answer 2

10x = 16(x-12)

10x = 16x - 192

-10x   -10x

0 = 6x - 192

+192    +192

192 = 6x

 6      6

x = 32 [minutes]

 

x-12 = 32 - 12 = 20

 

First set up an equation, since they are going to meet up, you will need to set both expressions equal to each other. 

So 10 mph * time, and 16 mph * (time - 12)

Now, distribute the 16 on the right side.

Next use the subtraction property to collect the "x"s and collect like terms.

Then move the 192 to the other side using the addition property.

Lastly, use the division property to divide by 6 and simplify to find that it will take a total of 32 minutes for them to meet, for the first cyclist.

 

***Do not forget to go back and put the 32 in for x to find that it will take the second cyclist 20 minutes [32 - 12] to catch up the first.