word problem

Question

 Spencer hiked up a trail in 3 hours. On his way back down, Spencer decided to take a different trail that was 1.5 miles longer. Hiking at the same speed on both trails, Spencer’s return trip took 3 hours and 30 minutes. How fast was Spencer hiking?

Answer 1

I'm not sure what level math you're in, but distance problems should always start off with r*t=d.

 

                 Rate                *                   time                            =          distance

going           x/3                                        3                                               x

back          (x+1.5)/3.5                             3.5                                            x+1.5

 

Since he hiked the trails at the same rate, you can set the rates equal to get the fractional equation

 

x  = (x+1.5)

3        3.5

 

Cross multiply to get

3.5x = 3x + 4.5      I distributed also

.5x   =   4.5

x      =   9

Go back to key and plug everything in

going is 3 mph for 3 hours which totals 9 miles.

back is 3mph for 3.5 hours which totals 10.5 miles.

 

hope this helped.

Answer 2

Let x = the distance Spencer hike up the trail from his home.

Then x+1.5= the distance he traveled back home

 

Since his speed is the same going both ways, then the equation can be set up in which is:

 

x/3=(x+1.5)/3.5. Note: 3 hours and 30 minutes is the same as 3.5 hours.

 

Solve for x to get the distance.

 

x/3=2/7*x+3/7 Note: 3.5=7/2 and 1.5/3.5=3/7

 

Multiply the equation by the least common denominator, being 21, to simplify the asthmatic.

 

 7x=  6x+9

-6x=-6x

   x=9

 

9/3=3

 

Hence, Spencer went 3 miles per hour both ways.