USING GRADIENT TO SOLVE WORD PROBLEMS WORKSHEET

Problem 1 :

The graph alongside indicates the distance run by a sprinter in a number of seconds.

a. Find the gradient of the line.

b. Interpret the gradient found in a.

c. Is the speed of the runner constant or variable? What evidence do you have for your answer?

Solution

Problem 2 :

The graph alongside indicates the distances travelled by a truck driver. Determine:

a. the average speed for the whole trip

b. the average speed from

i. O to A ii. B to C

c. the time interval over which the average speed is greatest.

Solution

Problem 3 :

The graph alongside indicates the wages paid to sales assistants.

a. What does the intercept on the vertical axis mean?

b. Find the gradient of the line. What does this gradient mean?

c. Determine the wages for working:

i. 6 hours ii. 18 hours

d. If no payment was made for not working but the same payment was made for 8 hours work, what would be the new rate of pay?

Solution

Problem 4 :

The graphs alongside indicate the fuel consumption and distance travelled at speeds of 60 kmph (graph A) and 90 kmph (graph B).

a. Find the slope of each line.

b. What do these slopes mean?

Solution

Problem 5 :

The graph alongside indicates the courier charge for distance travelled. 

a. What does the value at A indicate?

b. Find the gradients of the line segments AB and BC. What do these gradients indicate?

c. If a straight line segment was drawn from A to C, find its gradient. What would this gradient mean?

Solution