SOLUTION: Simultaneous equation Exercise 7: solving problem using simultaneous equation Q7: Challenge: Jacob travels from A to B, a distance of 410 km over 9 hours. Some of the time (sa

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 traveled at 40 km/h.
Ans:
If he travelled for x hours at 50 kmph and y hours at 40 kmph, we have 2 equations

x + y = 9 -----> (1) since total time is 9 hours
50*x + 40*y = 410 -----> (2) since total distance is 410 km

One way of solving the above is by elimination.
If the coefficients of either x or y is the same in both the eqns, we can
subtract one from the other to eliminate x or y and solve for the other
variable.

Multiply eqn (1) by 40 to make the coefficient of y also as 40. We get

40*x + 40*y = 360 -------> (3)

Subtract eqn (3) from eqn (1)

(50*x - 40*x) + (40*y - 40*y) = 410 - 360 = 50
10*x = 50
x = 5
Since x + y = 9, y = 4
So he travelled for 5 hours at 50 kmph, and 4 hours at 40 kmph
Check for correctness:
Total distance travelled = 5*50 + 4*40 = 250 + 160 = 410. Correct.
:)