30. A student travelled for x hours

Question

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

Answer 1

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.