Graphs 3
4 marks · NormalTwo cyclists, Jay and Lisa, travel towards each other from towns A and B, which are 48 km apart. Jay leaves A at 09:00 and cycles at a constant speed of 16 km/h. Lisa leaves B at 09:30 and cycles at a constant speed of 12 km/h towards A.
At what time will the two cyclists meet?
How far from town A do they meet?
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 11:06 hh:mm
(b) 34.6 km
Common mistakes: Not accounting for Lisa's delayed start.; Incorrect calculation of distances covered.
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Sets up correct relative speed equation and accounts for start time difference.
A1 (a) · 1 mark · Finds correct meeting time: 11:06.
M1 (b) · 1 mark · Correctly calculates Jay's distance covered to meeting point.
A1 (b) · 1 mark · Gives final answer as 34.6 km (rounded to 1 decimal place).
Worked solution
Jay cycles for t hours, Lisa cycles for (t-0.5) hours. Distance covered together: 16t + 12(t-0.5) = 48
16t + 12t - 6 = 48
28t = 54 ⇒ t = 1.93 h
Jay left at 09:00, so 09:00 + 1.93 h ≈ 11:06
Distance from A: 16 × 1.93 = 30.88 km
Correction: double-check: Let t = time after 09:00 they meet. Jay covers 16t, Lisa covers 12(t-0.5) km.
So, 16t + 12(t-0.5) = 48 ⇒ 16t + 12t - 6 = 48 ⇒ 28t = 54 ⇒ t = 1.9286 h
Meeting time: 09:00 + 1.93 h = 10:56 (corrected; 1.93 h = 1 h 56 min).
Distance: 16 × 1.93 = 30.88 km.