30. A student travelled for x hours
at 5km/hr and for y hours at
10km/hr. The journey was 35km
altogether, find x and y if the
average speed of the journey was
7km/hr.
A. 3hrs, 3hrs
B. 3hrs, 2hrs
C. 1 hr, 4hrs
D. 2hrs, 3hrs
Let's set up the equation to solve for x and y.
The total distance travelled is the sum of the distances travelled at each speed.
Distance travelled at 5km/hr: 5x
Distance travelled at 10km/hr: 10y
According to the problem, the total distance travelled is 35km. So we have the equation:
5x + 10y = 35
We also know that the average speed of the journey is 7km/hr. Average speed is total distance divided by total time.
Total distance = 35
Total time = x + y
So we have the equation:
35/(x+y) = 7
To simplify this equation, we can divide both sides by 7:
5/(x+y) = 1
Now we have a system of two equations:
5x + 10y = 35
5/(x+y) = 1
To solve this system, let's solve the second equation for x+y:
x+y = 5
Now we can use this value of x+y in the first equation to solve for x and y.
5x + 10y = 35
Substitute x+y = 5 into this equation:
5x + 10(5) = 35
5x + 50 = 35
5x = 35 - 50
5x = -15
x = -15/5
x = -3
Substitute this value of x into x+y = 5:
-3 + y = 5
y = 5 + 3
y = 8
However, since we are dealing with time, we cannot have negative values for x and y.
Therefore, the correct answer is not among the given options.
Answer: None of the above options.
To solve this problem, we can use the formula for average speed:
Average speed = Total distance / Total time
Given that the average speed is 7 km/hr and the total distance is 35 km, we can set up the equation as follows:
7 = 35 / (x + y)
Cross multiplying, we get:
7(x + y) = 35
Dividing both sides by 7, we have:
x + y = 5
Now we need to set up another equation based on the given information about the individual speeds and times:
x * 5 + y * 10 = 35
Simplifying, we have:
5x + 10y = 35
We can now solve this system of equations.
To do that, we'll multiply the first equation by 5 to eliminate the x coefficient:
5(x + y) = 5(5)
5x + 5y = 25
Now, we'll subtract this equation from the second equation:
(5x + 10y) - (5x + 5y) = 35 - 25
5y = 10
Dividing both sides by 5, we get:
y = 2
Substituting this value back into the first equation, we can solve for x:
x + 2 = 5
x = 3
Therefore, the values of x and y are 3 and 2 respectively.
So, the correct answer is option B: 3 hrs, 2 hrs.