Question
Train X leaves New York at 1 am and travels east at a constant speed of x mph. If train Z leaves New York at 2 am and travels east, at what constant rate of speed will train Z have to travel in order to catch train X at exactly 5.30 am ?
Answer: Option D
Let the speed of train Z be z mph
Distance travelled by train X in 1 hr = x miles
Relative speed of train Z w.r.t. train X = (z - x) mph
To catch train X at 5.30 am, train Z will have to cover x miles at relative speed in 3 hr 30 min, i.e., $$\frac{7}{2}$$ hrs
$$\eqalign{
& \therefore \left( {z - x} \right) \times \frac{7}{2} = x \cr
& \Rightarrow \frac{7}{2}z = \frac{9}{2}x \cr
& \Rightarrow z = \left( {\frac{9}{2} \times \frac{2}{7}} \right)x \cr
& \Rightarrow z = \frac{9}{7}x \cr} $$
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Let the speed of train Z be z mph
Distance travelled by train X in 1 hr = x miles
Relative speed of train Z w.r.t. train X = (z - x) mph
To catch train X at 5.30 am, train Z will have to cover x miles at relative speed in 3 hr 30 min, i.e., $$\frac{7}{2}$$ hrs
$$\eqalign{
& \therefore \left( {z - x} \right) \times \frac{7}{2} = x \cr
& \Rightarrow \frac{7}{2}z = \frac{9}{2}x \cr
& \Rightarrow z = \left( {\frac{9}{2} \times \frac{2}{7}} \right)x \cr
& \Rightarrow z = \frac{9}{7}x \cr} $$
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