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# An Aero Plane Travelled a Distance of 400 Km at an Average Speed of X Km/Hr. on the Return Journey, the Speed Was Increased by 40 Km/Hr. Write Down an Expression for the Time Tak - ICSE Class 10 - Mathematics

#### Question

An Aero plane travelled a distance of 400 km at an average speed of x km/hr. On the return journey, the speed was increased by 40 km/hr. Write down an expression for the time taken for:
(1) the onward journey;
(2) the return journey.
If the return journey took 30 minutes less than the onward journey, write down an equation in x and find its value.

#### Solution

Distance = 400 km

The average speed of the aeroplane = x km/hr

Speed while returning = (x + 40) km/hr

1) We know : "Time" = "Distance"/"Speed"

Time taken for onward journey = 400/x hrs

2) Time taken for return journey  = 400/(x + 40) hrs

From the given information we have

400/x - 400/(x + 40) = 30/60

(400x + 16000 - 400x)/(x(x + 40)) = 1/2

16000/(x(x + 40)) = 1/2

x^2 + 40x - 32000 = 0

x^2 + 40x - 32000 = 0

x^2 + 200x - 160x - 32000 = 0

x(x + 20) - 160(x + 2000) = 0

(x + 200)(x - 160) = 0

x = -200, 160

Since speed cannot be negative. Thus x = 160

Is there an error in this question or solution?

#### APPEARS IN

Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6E | Q: 4

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Solution An Aero Plane Travelled a Distance of 400 Km at an Average Speed of X Km/Hr. on the Return Journey, the Speed Was Increased by 40 Km/Hr. Write Down an Expression for the Time Tak Concept: Quadratic Equations.
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