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05 Jul 2020, 04:38
Kudos
Bookmarks
Let Harriet take x minutes to drive from A-ville to B-town
\(\frac{115}{60}*(x) = \frac{135}{60}*(300-x)\)
Solving for \(x\),
\(x=162\)
Answer: D
\(\frac{115}{60}*(x) = \frac{135}{60}*(300-x)\)
Solving for \(x\),
\(x=162\)
Answer: D
27 Jan 2026, 15:08
Kudos
Bookmarks
Deconstructing the Question
Harriet makes a round trip (A to B and back to A).
This means the Distance is Constant.
We are given the total time (5 hours) and the two speeds. The most efficient way to solve this is using the Ratio Method to avoid complex fractions.
Step 1: Establish the Ratios
First, find the ratio of the speeds and simplify it.
\(S_1 : S_2 = 115 : 135\)
Divide both sides by 5:
\(S_1 : S_2 = 23 : 27\)
Since Distance is constant, Time is inversely proportional to Speed.
\(T_1 : T_2 = 27 : 23\)
Step 2: Determine the Value of the Ratio Units
The total trip consists of \(27 + 23 = 50\) "units" of time.
We know the actual total time is 5 hours, which is \(5 \times 60 = 300\) minutes.
Equating the units to real time:
\(50 \text{ units} = 300 \text{ minutes}\)
\(1 \text{ unit} = \frac{300}{50} = 6 \text{ minutes}\)
Step 3: Calculate the Specific Time Requested
The question asks for the time to drive from A-ville to B-town (the first leg).
Based on our inverted ratio, \(T_1\) corresponds to 27 units.
\(Time_{A \to B} = 27 \text{ units} \times 6 \text{ minutes/unit}\)
\(Time_{A \to B} = 162 \text{ minutes}\)
Answer: D
Harriet makes a round trip (A to B and back to A).
This means the Distance is Constant.
We are given the total time (5 hours) and the two speeds. The most efficient way to solve this is using the Ratio Method to avoid complex fractions.
- Speed A to B (\(S_1\)): 115 km/h
- Speed B to A (\(S_2\)): 135 km/h
- Total Time: 5 hours (300 minutes)
Step 1: Establish the Ratios
First, find the ratio of the speeds and simplify it.
\(S_1 : S_2 = 115 : 135\)
Divide both sides by 5:
\(S_1 : S_2 = 23 : 27\)
Since Distance is constant, Time is inversely proportional to Speed.
\(T_1 : T_2 = 27 : 23\)
Step 2: Determine the Value of the Ratio Units
The total trip consists of \(27 + 23 = 50\) "units" of time.
We know the actual total time is 5 hours, which is \(5 \times 60 = 300\) minutes.
Equating the units to real time:
\(50 \text{ units} = 300 \text{ minutes}\)
\(1 \text{ unit} = \frac{300}{50} = 6 \text{ minutes}\)
Step 3: Calculate the Specific Time Requested
The question asks for the time to drive from A-ville to B-town (the first leg).
Based on our inverted ratio, \(T_1\) corresponds to 27 units.
\(Time_{A \to B} = 27 \text{ units} \times 6 \text{ minutes/unit}\)
\(Time_{A \to B} = 162 \text{ minutes}\)
Answer: D
