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If the city B lies along a certain route between A and C, what is the

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If the city B lies along a certain route between A and C, what is the  [#permalink]

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New post 01 Jul 2017, 10:23
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If the city B lies along a certain route between A and C, what is the distance from A to B?

(1) Travelling from C to A at an average rate of 45 m.p.h. takes 25 minutes longer than at an average rate of 50 m.p.h.

(2) Traveling along the route at a constant 25 miles per gallon of gas, a car will use twice as much gas between A and B as it will use between B and C

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If the city B lies along a certain route between A and C, what is the  [#permalink]

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New post 01 Jul 2017, 11:21
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ydmuley wrote:
If the city B lies along a certain route between A and C, what is the distance from A to B?

(1) Travelling from C to A at an average rate of 45 m.p.h. takes 25 minutes longer than at an average rate of 50 m.p.h.

(2) Traveling along the route at a constant 25 miles per gallon of gas, a car will use twice as much gas between A and B as it will use between B and C

Kudos for correct solution.


Let Distance from \(A\) to \(C\) \(= D\). Distance from \(A\) to \(B\) \(= D_1\) and Distance from \(B\) to \(C\) \(= D_2\)

We need to find \(D_1\).

(1)Travelling from C to A at an average rate of 45 m.p.h. takes 25 minutes longer than at an average rate of 50 m.p.h.
Let time taken with speed 50 m.p.h \(= t\)

\(D = 50*t\) ----------- (i)

\(D = 45(t+\frac{5}{12})\) -----------(ii) --------- (\(25\) mins \(= \frac{5}{12} hr\))

Equating (i) and (ii);

\(50t = 45(t+\frac{5}{12}) =45t + \frac{45*5}{12}\)

\(50t - 45t = \frac{15*5}{4}\) \(=>\) \(5t = \frac{15*5}{4}\)

\(t = \frac{15}{4}\) hours

\(D = 50 * \frac{15}{4} = 187.5\) miles

Does not have any information about distance from A to B or B to C. Hence I is Not Sufficient.

(2) Traveling along the route at a constant 25 miles per gallon of gas, a car will use twice as much gas between A and B as it will use between B and C. ( twice as much gas means twice the time.) Let time taken to travel from \(B\) to \(C = t_1\)

\(D_1 = 25*2t_1 => 25 = \frac{D_1}{2t_1}\) ---------- (iii)

\(D_2 = 25*t_1 => 25 = \frac{D_2}{t_1}\) ----------- (iv)

Equating (iii) and (iv), we get; \(\frac{D_1}{2t_1} = \frac{D_2}{t_1}\)\(=>\) \(D_2 = \frac{D_1}{2}\)

Cannot find Distance from A to B. Hence II is Not Sufficient.

Combining (1) and (2);

\(D_1 + D_2 = D\)

\(D_1 + \frac{D_1}{2} = D\)

\(\frac{2D_1 + D_1}{2} = D\)

\(3D_1 = 2D\)

\(D_1 = \frac{2}{3}D\)

\(D_1 = \frac{2}{3} * 187.5 = 125\) miles .

Answer (C)...
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If the city B lies along a certain route between A and C, what is the   [#permalink] 01 Jul 2017, 11:21
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