A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less, it would have needed 6 hours more. The distance, in km, travelled by the train is
Question:
A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less, it would have needed 6 hours more. The distance, in km, travelled by the train is
A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less, it would have needed 6 hours more. The distance, in km, travelled by the train is
Options
Answer: 720
Explanation:
Step 1: Let variables Let: Distance = D km Original speed = V km/h Original time = T hours → D = V × T We are given two scenarios: Speed increased by 6 → time decreased by 4: D=(V+6)(T−4)D = (V + 6)(T - 4)D=(V+6)(T−4) Speed decreased by 6 → time increased by 6: D=(V−6)(T+6)D = (V - 6)(T + 6)D=(V−6)(T+6) Step 2: Write equations From original: D = V × T Equation 1: V × T = (V + 6)(T − 4) → VT = VT − 4V + 6T − 24 → −4V + 6T − 24 = 0 → 6T − 4V = 24 → 3T − 2V = 12 Equation 2: V × T = (V − 6)(T + 6) → VT = VT + 6V − 6T − 36 → 6V − 6T − 36 = 0 → V − T − 6 = 0 → V − T = 6 Step 3: Solve the system Equations: 3T − 2V = 12 V − T = 6 → V = T + 6 Substitute V = T + 6 into first: 3T − 2(T + 6) = 12 → 3T − 2T − 12 = 12 → T − 12 = 12 → T = 24 Then V = T + 6 = 24 + 6 = 30 km/h Step 4: Find distance D = V × T = 30 × 24 = 720 km ✅ Answer 720
Explanation:
Step 1: Let variables Let: Distance = D km Original speed = V km/h Original time = T hours → D = V × T We are given two scenarios: Speed increased by 6 → time decreased by 4: D=(V+6)(T−4)D = (V + 6)(T - 4)D=(V+6)(T−4) Speed decreased by 6 → time increased by 6: D=(V−6)(T+6)D = (V - 6)(T + 6)D=(V−6)(T+6) Step 2: Write equations From original: D = V × T Equation 1: V × T = (V + 6)(T − 4) → VT = VT − 4V + 6T − 24 → −4V + 6T − 24 = 0 → 6T − 4V = 24 → 3T − 2V = 12 Equation 2: V × T = (V − 6)(T + 6) → VT = VT + 6V − 6T − 36 → 6V − 6T − 36 = 0 → V − T − 6 = 0 → V − T = 6 Step 3: Solve the system Equations: 3T − 2V = 12 V − T = 6 → V = T + 6 Substitute V = T + 6 into first: 3T − 2(T + 6) = 12 → 3T − 2T − 12 = 12 → T − 12 = 12 → T = 24 Then V = T + 6 = 24 + 6 = 30 km/h Step 4: Find distance D = V × T = 30 × 24 = 720 km ✅ Answer 720
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