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).

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