SOLUTION: A biker decided to cover the distance of 120 km at a certain speed. However, he actually went 6 km/h slower so he arrived at his destination 1 hour later than he wanted to. What wa

Question 1029152: A biker decided to cover the distance of 120 km at a certain speed. However, he actually went 6 km/h slower so he arrived at his destination 1 hour later than he wanted to. What was the actual speed of the biker?
PS:If x is the actual speed of the biker, then what is the equation?
Found 5 solutions by ikleyn, mananth, josgarithmetic, josmiceli, MathTherapy:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
A biker decided to cover the distance of 120 km at a certain speed. However, he actually went 6 km/h slower
so he arrived at his destination 1 hour later than he wanted to. What was the actual speed of the biker?
PS:If x is the actual speed of the biker, then what is the equation?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let x be the actual speed of the biker, in . Then his planned speed was (x+6). So he planned to spend hours, but actually spent , which is in 1 hour more. Thus you have this equation - = 1. To solve it for x , multiply both sides by x*(x+6). You will get 120*(x+6) -120x = x*(x+6), or 120*6 = x*(x+6), or = . Factor left sides: (x-24)*(x+30) = 0. The roots are x = 24 and x = -30. Only positive x = 24 fits. Answer. The actual speed of the biker is 24 . Please check it yourself.

Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
A biker decided to cover the distance of 120 km at a certain speed.
let speed be x
Time he would take = 120/x ( t=d/r)
However, he actually went 6 km/h slower
Actually his speed was 6 km slower (x-6)
Time taken =120/(x-6)

so he arrived at his destination 1 hour later
120/(x-6) -120/x = 1
Simplify
120x -120(x-6) = x(x-6)
120x -120x +720=x^2-6x
x^2-6x-720=0
x^2-30x+24x-720=0
x(x-30)+24(x-30)=0
(x-30)(x+24)=0
x= 30 OR -24
Ignore negative
planned speed = 30 km/h
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

RATE TIME DISTANCE Expected x t 120 Actual x-6 t+1 120

That arrangement of data is not exactly as you say you wanted, so according to your "PS", change the data table and assigning to THIS instead:

RATE TIME DISTANCE Expected x+6 t 120 Actual x t+1 120

This new arrangement might or might not be a better one than the first one; but continuing this way, make a system of equations.

Begin to solve.
----maybe still not the best way to continue.

The system is not linear. Try to solve for one variable in terms of the other and substitute into the other equation.

-

You continue this until solved.
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the actual speed of the biker in km/hr
Let = the time in hrs he would normally take
to arrive traveling at speed
--------------------------------
Equation for riving on time:
(1)
Equation for arriving 1 hr late:
(2)
--------------------------
(1)
substitute (1) into (2)
(2)
(2)
(2)
(2)
Multiply both sides by
(2)
Complete the square
(2)
(2)
(2)
Take the square root of both sides
(2)
(2)
The actual speed of the biker is 30 km/hr
-----------------
check:
(1)
(1)
(1) hrs
and
(2)
(2)
(2)
(2)
(2)
(2) hrs
OK
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

A biker decided to cover the distance of 120 km at a certain speed. However, he actually went 6 km/h slower so he arrived at his destination 1 hour later than he wanted to. What was the actual speed of the biker?
PS:If x is the actual speed of the biker, then what is the equation?

Since actual speed was x, then planned speed was: x + 6
Time taken to cover distance at actual speed:
Time it would�ve taken to cover distance at planned speed:
The following TIME equation is thus formed:
120(x + 6) = 120x + x(x + 6) -------- Multiplying by LCD, x(x + 6)

(x - 24)(x + 30) = 0
x, or ACTUAL speed was: OR x = - 30 (ignore)
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