Question

What is the time difference between City A and City B?

• A. 1 hour and 30 minutes
• B. 2 hours
• C. 2 hours and 30 minutes
• D. 1 hour
• E. Cannot be determined
• A. 700
• B. 550
• C. 600
• D. 500
• J. Cannot be determined

Answer 1

The Correct Option is B

Distance between A and B = 3000 km. Wind speed = 50 km/h from east to west. Let cruising speed of the plane = \( v \) km/h. From B to A: effective speed = \( v + 50 \), travel time in actual hours = \( \frac{3000}{v+50} \).
From A to B: effective speed = \( v - 50 \), travel time in actual hours = \( \frac{3000}{v-50} \).
From schedule: B to A: Dep 8:00 am (B local), Arr 3:00 pm (A local) → elapsed local time = 7 hours.
A to B: Dep 4:00 pm (A local), Arr 8:00 pm (B local) → elapsed local time = 4 hours.
Let time difference (A ahead of B) = \( t \) hours.
Travel B→A: Actual travel time = \( 7 - t \) hours.
Travel A→B: Actual travel time = \( 4 + t \) hours.
Equations: \[ \frac{3000}{v+50} = 7 - t, \] \[ \frac{3000}{v-50} = 4 + t. \] Solving: from first, \( v+50 = \frac{3000}{7-t} \), from second, \( v-50 = \frac{3000}{4+t} \). Subtract: \[ 100 = 3000\left( \frac{1}{7-t} - \frac{1}{4+t} \right), \] \[ \frac{1}{7-t} - \frac{1}{4+t} = \frac{1}{30}. \] Simplify: \[ \frac{(4+t)-(7-t)}{(7-t)(4+t)} = \frac{-3+2t}{(7-t)(4+t)} = \frac{1}{30}. \] So: \[ -3 + 2t = \frac{(7-t)(4+t)}{30}. \] Multiply: \[ -90 + 60t = 28 + 3t - t^2. \] Rearrange: \[ t^2 + 57t - 118 = 0. \] Solving, positive root: \( t = 2 \) hours.

Answer 2

From Q11: \( t = 2 \) hours. B→A: actual travel time = \( 7 - 2 = 5 \) hours → \( v + 50 = \frac{3000}{5} = 600 \) → \( v = 550 \) Wait — check carefully.
Re-check: B→A: Dep 8:00 B local, Arr 3:00 A local. Time difference 2 hours (A ahead) → arrival time in B local = 1:00 pm → elapsed actual = 5 hours. So \( v+50 = 3000/5 = 600 \) → \( v = 550 \).
A→B: Dep 4:00 pm A local = 2:00 pm B local, Arr 8:00 pm B local → elapsed = 6 hours, so \( v - 50 = 3000/6 = 500 \) → \( v = 550 \). Hence \( v = 550 \) km/h. So Correct Answer is (2).