Dyani & Tim, Front & Main Sts.

Dyani and Tim are each walking at a constant speed along Front and Main Streets, respectively, which are perpendicular. When Dyani is at the intersection, Tim is still 500 yards away. In two minutes they are equidistant from the intersection. In eight more minutes they are again equidistant from the intersection. What’s the ratio of Dyani’s speed to Tim’s speed?

1. 4:5
2. 5:6
3. 2:3
4. 5:8
5. 1:2

Show/Hide Solution

Let D’s speed = d and Tim’s speed = t

in yards per minute: yd/min.

Let T₀ be Tim’s position at time = 0, etc.

T₀ = 500 yd.
T₀T₂ = 2t
So T₂O = 500 – 2t
T₀T₁₀ = 10 t
So OT₁₀ = 10t – 500

D₀O = 0
OD₂ = 2d (= 500 – 2t)
OD₁₀ = 10d (= 10t – 500)

2d = 500 – 2t → 2d + 2t = 500
10d = 10t – 500 → 10d – 10t = -500

2d + 2t = 500	→ x 5 →	10d + 10t = 2500
		10d – 10t = -500
		20d = 2000	→ d = 100 yd/min (≈ 3.4 mi/hr)

2(100) + 2t = 500 → 2t = 300 → t = 150 yd/min (≈ 5.1 mi/hr)

So d:t = 100:150 = 2:3. The answer is (c).