Hi Guys,
It's a DS question and we don't need to calculate the actual distance between Houghton and Callahan; just the analysis that the information provided in the statements is sufficient is enough to answer our question.
Analyze the Given Info:The question asks us if the information provided in the statements is sufficient to calculate the distance between two places. We know that
Distance = Speed * Time. So, if we are given the values of speed & time taken, we can find the distance between the places. Let's evaluate the information given in the statements to see if it provides us the required information.
Analyze statement-I independentlySt-I gives us two scenarios of speed & time taken to cover the same distance. Let's write equations for both the scenarios:
a. Time taken to cover the distance at a speed of \(55 \frac{miles}{hour} = \frac{D}{55}\) assuming the distance between Houghton and Callahan to be D.
b. Time taken to cover the same distance at a speed of \(50 \frac{miles}{hour} = \frac{D}{50}\).
Since we know that the difference between the time taken is 1 hour, we can write \(\frac{D}{50} - \frac{D}{55} = 1\).
From this equation, we can easily find out a unique value of D. Hence, statement-I is sufficient to answer the question.
Analyze statement-II independentlySt-II tells us that it takes 11 hours to cover half the distance at a speed of 25 miles/hour. So, we can write \(\frac{D}{2} = 11* 25\).
Again, this equation would give us a unique value of D. Hence, statement-II alone is sufficient to answer the question.
It's important to remember that DS question does not ask us to find the actual value of the unknown. Once we deduce that the information provided in the statements is sufficient to find out a unique value of the unknown, we should not be doing further calculations to save our time.Regards
Harsh
_________________