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. :)