Question

Cities A and B are 400 miles apart. Linda starts from A at 7 a.m. and travels towards B at 40 mph. Mathew starts from B at 8 a.m. and travels towards A at 60 mph. At what time do they meet?

• A. 10:15 a.m.
• B. 11:45 a.m.
• C. 11:36 a.m.
• D. 12:00 a.m.

Answer 1

The correct option is C 11:36 a.m.


Let's assume they are meeting at a distance x from city A.


Mathew travels for time t.
Linda travels for time t + 1 (1 hour more than Mathew).

Linda's speed = 40 mph
Distance traveled = x
Time = t + 1

We know,
$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

$\Rightarrow \text{40}=\frac{\text{x}}{\text{t + 1}}$

⇒ x = 40(t + 1)

Mathew's speed = 60 mph
Distance traveled = 400 – x
Time = t

$\Rightarrow \text{60}=\frac{\text{400 – x}}{\text{t}}$

⇒ 60t = 400 – x
⇒ 60t = 400 – 40(t + 1)
⇒ 60t + 40t = 400 – 40
⇒ 100t = 360
⇒ t = 3.6 hours

Now,
3.6 hour = 3 hour + 0.6 × 6 = 3 hour and 36 minutes

So, they will meet at
= 8:00 a.m. + 3 hour + 36 minutes
= 11:36 a.m.