Terry bicycles for 1/4 at an average speed of x km/hr. He then cycles for 1/3 hour at an average speed of x+10 km/hr. he cycles a total distance of 15 km. work out the value of x.
(1/4)x + (1/3)(x+10) = 15
(7/12)x = 15 - 10/3 = 35/3
(1/12)x = 5/3
x = 60/3 = 20
To solve this problem, we can use the formula:
Distance = Speed × Time
Let's break down the question into two parts:
1) In the first part of the journey, Terry cycles for 1/4 hour (or 0.25 hours) at an average speed of x km/hr.
For this part of the journey, the distance Terry travels can be calculated as: distance1 = x km/hr × 0.25 hr
2) In the second part of the journey, Terry cycles for 1/3 hour (or 0.33 hours) at an average speed of (x+10) km/hr.
For this part of the journey, the distance Terry travels can be calculated as: distance2 = (x+10) km/hr × 0.33 hr
Now, we know that the total distance Terry cycles is 15 km:
distance1 + distance2 = 15 km
Substituting the formulas for distance1 and distance2, we get:
(x km/hr × 0.25 hr) + ((x+10) km/hr × 0.33 hr) = 15 km
Now, let's solve this equation to find the value of x.
0.25x + 0.33(x+10) = 15
First, distribute the 0.33 to x and 10:
0.25x + 0.33x + 3.3 = 15
Combine like terms:
0.58x + 3.3 = 15
Subtract 3.3 from both sides:
0.58x = 11.7
Divide both sides by 0.58:
x = 20.17
Therefore, the value of x is approximately 20.17 km/hr.