If Terry hiked 0.5km/h faster, he would have taken 1h less to complete a 15- km hike. What was Terry's hiking speed?
At the higher speed,
15 = (T-1)*(V+0.5)= VT +.5T -V -.5
and at the speed that he used,
15 = VT
Combining the two equations results in
.5T -V = 0.5
.5T -15/T = 0.5
Turn that into a quadratic by multiplying both sides by 2T
T^2 -T -30 = 0
(T-6)(T+5) = 0
T = 6 hours
V = 15/6 = 2.5 km/hour
THANK YOU!!!!!
To find Terry's hiking speed, we can use the formula: speed = distance / time.
Let's assume Terry's original hiking speed is x km/h.
According to the problem, if Terry hiked 0.5 km/h faster, his new speed would be (x + 0.5) km/h.
Now, with Terry's original speed, it took him a certain amount of time to complete the 15 km hike. Let's say it took him t hours.
Therefore, using the formula, we have:
speed = distance / time
x = 15 km / t hours
If he hiked 0.5 km/h faster, it would take him 1 hour less to complete the hike. So, his new time would be (t - 1) hours.
Again using the formula, we have:
(x + 0.5) = 15 km / (t - 1) hours
Now, we have a system of two equations:
x = 15 km / t hours
x + 0.5 = 15 km / (t - 1) hours
We can solve this system of equations to find the value of x, which represents Terry's original hiking speed.
Here are the steps to solve the system of equations:
1. Simplify the second equation by multiplying both sides by (t - 1):
(x + 0.5)(t - 1) = 15 km
2. Expand the left side of the equation:
xt - x + 0.5t - 0.5 = 15 km
3. Group the like terms:
xt + 0.5t - x - 0.5 = 15 km
4. Rearrange the equation:
xt - x + 0.5t = 15.5 km
5. Substitute the value of x from the first equation into the second equation:
(15 km / t hours) * t - (15 km / t hours) + 0.5t = 15.5 km
6. Simplify the equation:
15 km - (15 km / t hours) + 0.5t = 15.5 km
7. Multiply both sides of the equation by t to eliminate the fraction:
15 km * t - (15 km / t hours) * t + 0.5t * t = 15.5 km * t
8. Simplify the equation:
15 km * t - 15 km + 0.5t^2 = 15.5 km * t
9. Subtract 15 km * t from both sides:
0.5t^2 - 15 km + 0.5t^2 - 15.5 km * t = 0
10. Combine like terms:
0.5t^2 - 15 km - 15.5 km * t = 0
11. Rearrange the equation in standard quadratic form:
0.5t^2 - 15.5 km * t - 15 km = 0
Now, you can solve this quadratic equation using various methods such as factoring, completing the square, or using the quadratic formula. Once you find the value of t, you can substitute it back into the first equation (x = 15 km / t) to find Terry's hiking speed.