4.3. Forming quadratic equations from a rate and speed word problem
N4. Rate and speed

Question

A man was driving his car from point A to point C in the countryside. After he has travelled for 70 km, at a constant speed of $x$ km/h, he reached point B, where his car tyre got punctured.

(a) Write down an expression, in terms of $x$ , for the time in hours, taken for him to drive from A to B. [1]

He then walks the remaining 8 km from B to C at a constant speed of ( $x$ – 60) km/h.

(b) Write down an expression, in terms of $x$ , for the time in hours, taken for him to walk from B to C. [1]

(c) The man took 4 hours to travel from A to C. Write down an equation in $x$ and show it reduces to $2x^2 - 159x + 2100 = 0$ . [3]

(d) Solve the equation $2x^2 - 159x + 2100 = 0$ . [3]

(e) Find how long it would have taken if the man was able to drive from A to C at the original constant speed. Give your answer in hours and minutes, correct to the nearest ten minutes. [2]

Solution

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distance, factorisation, quadratic equations, solve quadratic equations, time

4.3. Forming quadratic equations from a rate and speed word problem N4. Rate and speed

4.3. Forming quadratic equations from a rate and speed word problem
N4. Rate and speed