SOLUTION: Evan went on a bike ride of 120 miles. He realized that if he had gone 18 mph faster, he would have arrived 15 hours sooner. How fast did he actually ride?

Question 1139188: Evan went on a bike ride of 120 miles. He realized that if he had gone 18 mph faster, he would have arrived 15 hours sooner. How fast did he actually ride?

Found 4 solutions by josgarithmetic, ikleyn, josmiceli, greenestamps:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!

SPEED TIME(hours) DISTANCE ACTUAL r 120 IF r+18 120

-

Answer by ikleyn(52884)   (Show Source): You can put this solution on YOUR website!
.

            It is a standard problem to be solved using the "time" equation.

            It was solved tens (if not hundred) times at this forum, so I will be short.

Let "r" be the actual speed, in miles per hour. Then the hypothetical speed is (r+18) mph. The "time" equation is - = 15 hours. Cancel the factor 15 in both sides - = 1. Now multiply both sides by r*(r+18), simplify and solve for "r" 8*(r+18) - 8r = r*(r+18). 8*18 = r*(r+18) r^2 + 18r - 144 = 0 (r-6)*(r+24) = 0. There are two roots, 6 and -24, and only positive value of r= 6 is the solution to the problem. ANSWER. Actual speed was 6 mph. (Not much . . .)

Solved.

----------------

Using "time" equation is the STANDARD method of solving such problems.
From my post, learn on how to write, how to use and how to solve a "time" equation.

To see many other similar solved problems, look into the lessons
    - Had a car move faster it would arrive sooner
    - How far do you live from school?
    - Earthquake waves
    - Time equation: HOW TO use, HOW TO write and HOW TO solve it
in this site.

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the speed he actually went
(1)
(2)
-------------------------------------
(2)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)

and

He rode 6 mi/hr
---------------------
check:
(1)
(1)
(1)
(1)
(1)

Answer by greenestamps(13209)   (Show Source): You can put this solution on YOUR website!

An algebraic solution....

let x be the speed he rode at
Then x+18 is the speed he could have ridden at

The times to go 120 miles at the two speeds are 120/x and 120/(x+18).

The problem says the time would be 15 hours less at the higher speed:

x = -24 (nonsense) or x = 6

His actual speed was 6mph. (A very slow bicycle speed!)

CHECK:
120/6 = 20
120/(6+18) = 120/24 = 5
20-5 = 15

An informal solution -- if algebra is not required....

Make a list of pairs of numbers whose product is 120 and find two pairs that meet the conditions of the problem.

1*120
2*60
3*40
4*30
5*24
6*20
8*15
10*12

The pairs 5*24 and 6*20 satisfy the given conditions: 6+18 = 24; 20-5 = 15.
RELATED QUESTIONS
Darius went on a bike ride of 48 miles. He realized that if he had gone 6 mph faster, he... (answered by josgarithmetic,stanbon)
Colton went on a bike ride of 36 miles. He realized that if he had gone 3 mph faster, he... (answered by ankor@dixie-net.com)
Chris went on a bike ride of 24 miles. He realized that if he had gone 6 mph faster, he... (answered by Theo,MathTherapy)
Diego went on a bike ride of 90 miles. He realized that if he had gone 10 mph faster, he... (answered by josgarithmetic)
Miguel went on a bike ride of 24 miles. He realized that if he had gone 6 mph faster, he... (answered by josmiceli,ikleyn,MathTherapy)
Miguel went on a bike ride of 24 miles. He realized that if he had gone 6 mph faster, he... (answered by Alan3354,ikleyn)
Warren went on a bike ride of 60 miles. He realized that if he had gone 25 mph faster, he (answered by josgarithmetic)
Cameron went on a bike ride of 40 miles. He realized that if he had gone 8 mph faster, he (answered by josgarithmetic,ikleyn,greenestamps)
Zeke's motor cycle traveled 270 miles at a certain speed. Had he gone 15 mph faster, the... (answered by drk)