Julio covers the first \(r\) miles of his journey at \(x\) miles per hour and the last \(s\) miles of his journey at

[Gmat_mission]

Julio covers the first \(r\) miles of his journey at \(x\) miles per hour and the last \(s\) miles of his journey at \(y\) miles per hour. Is the time taken to cover the first \(r\) miles of the journey greater than the time taken to cover the last \(s\) miles of his journey?

A) \(r\) is \(10\) greater than \(s.\)
B) \(x\) is \(10\) greater than \(y.\)

Answer: E

Source: e-GMAT

[deloitte247]

Time = distance/speed
Time taken to cover r miles = r/x
Time taken to cover last 'S' miles = s/y

Target question => Is the time taken to cover the first r miles of the journey greater than the time taken to cover the last 'S' miles of his journey? i.e rs r/x > s/y

Statement 1 => r is 10 greater than s
r = 10 + s but there is no information about the value of x and y so statement 1 is NOT SUFFICIENT

Statement 2 => x is 10 greater than y
x = 10 + y but there is no information about the value of r and s so statement 2 is NOT SUFFICIENT

Combining both statements together =>
$$r=10+s\ and\ x=10+y$$
$$\frac{10+s}{10+y}>\frac{s}{y}$$
$$y\left(10+s\right)>s\left(10+y\right)\ =>\ \frac{10y+sy}{sy}>\frac{10s+sy}{sy}$$
$$\frac{10y}{10}>\frac{10s}{10}$$
$$y>s$$
$$The\ value\ of\ y\ and\ s\ is\ unknown\ so\ both\ statemets\ combined\ together\ is\ NOT\ SUFFICIENT$$
$$Answer\ =\ E$$