Question

Jacob travels from A to B, a distance of 410 km over 9 hours. Some of the time (say x hours) Jacob travelled at a speed of 50 km/h, and for the rest of time (say y hours) he travelled at 40 km/h.

Find the number of hours he travelled at 40 km/h.

Answer 1

Explanation:

Let's use the formula:

distance = speed × time

We can use this formula to set up two equations with two unknowns, x and y, representing the time Jacob spent traveling at 50 km/h and 40 km/h, respectively.

At 50 km/h, Jacob covered a distance of 50x km.

At 40 km/h, Jacob covered a distance of 40y km.

Together, these distances add up to the total distance of 410 km:

50x + 40y = 410

We also know that Jacob spent a total of 9 hours traveling:

x + y = 9

Now we have two equations with two unknowns. We can solve for one of the variables in one equation, and substitute that expression into the other equation. For example, we can solve the second equation for x:

x = 9 - y

Substituting this expression for x into the first equation, we get:

50(9 - y) + 40y = 410

Expanding and simplifying:

450 - 50y + 40y = 410

10y = 40

y = 4

Therefore, Jacob traveled at 40 km/h for 4 hours, and at 50 km/h for the remaining 5 hours (since x + y = 9).