If Terry had hiked 0.5km/h faster; he would have taken 1 hour less to complete a...

K

Kendokid

New member
...15km course whats his speed? I need a step by step solution to solve that, the answer is in the back of the book but I want to know what to do.
 
Let Terry's speed = x km/h
Time taken to complete 15 kms course = 15/x hours
If Terry's speed is hiked by 0.5 km/h i.e., x+0.5 km/h
Time taken to complete 15 kms course = 15/(x+0.5) hours
According to the question
15/(x+0.5) = 15/x - 1
15/(x+0.5) = (15-x)/x
By cross multiplication
(15)*(x) = (15-x)*(x+0.5)
15x = 15x + 7.5 - x^2 - 0.5x
x^2 + 15x - 15x - 0.5x - 7.5 = 0
x^2 - 0.5x - 7.5 = 0
x^2 - 3x + 2.5x - 7.5 = 0
x(x - 3) + 2.5(x - 3) = 0
(x - 3) ( x + 2.5) = 0
When x-3=0 , x=3 and when x+2.5=0 , x= - 2.5
In this case x value i.e., speed cannot be negative
Therefore x = 3 shall be taken
Terry' speed = 3 km/h
 
Assume Terry took "n" hours with a speed of "s" to cover 15 kms.
Since speed = distance/time, it means that

s = 15/n ...........eq(1)
or, 15 = s*n ......eq(2)

Now if his speed is (s+0.5) he takes (n-1) hours to cover the same distance.
15 = (s+0.5)*(n-1).......eq(3)

combining equation 2 and 3 above,
(s+0.5)*(n-1) = s*n
or, s*n -s + 0.5n - 0.5 = s*n
or, s - 0.5n + 0.5 = 0

(putting value of s from eq(1))

or, 15/n - 0.5n + 0.5 = 0

(multiply both sides by 2n)

or, 30 - n^2 +n = 0
or, n^2 -n -30 = 0
or, (n-6)(n+5) = 0
so n = 6 or -5 , but since time can't be negative we discard the negative value. Hence n =6.
Putting value of n in eq(1)
s = 15/6 = 2.5

That is the speed of Terry was 2.5 Km/Hour
 
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