Elliot began the journey at 8 a.m. at 40 kilometers per hours. Benita began to chase him at 11 a.m. at 50?

Question

kilometers per hour. What time was it when Benita got within 60 kilometers of Elliot?

(Answer: 5 p.m.) Please show your work. Thank you!

Answer 1

Elliot has traveled 120 km when Benita starts at 11 AM (40 km/h * 3 h)
If you add 40 km to Elliot's total and 50 km to Benita total for each subsequent hour, stopping when the difference is 60, you will find the time. Like so:

Time----- Elliot-------- Benita-----Difference
11---------120 ----------0 ----------120
12---------160 ---------50 ---------110
1-----------200---------100 ---------100
2-----------240---------150 ----------90
3 ----------280----------200 ---------80
4-----------320----------250 --------70
5-----------360----------300 ---------60

As you can see, the time is 5 PM when Benita is within 60 km of Elliot.

Answer 2

Since she's going 10 kph faster than him, she gets 10 km closer every hour. But he got a 3-hour head start, which at 40 kph put him 120 km ahead when she started. She needed to get 60 km closer to him to be within 60 km, and catching up at the rate of 10 kph, it took her 6 hours to do it. 11:0 + 6 hours = 17:00 or 5 PM.