The distance between 2 town x and y, is 50km.alan drive from x to y at an average speed of vkm/ h.
Write down an expression,in term of v,for the time in hour, that he took to complete the journey from x to y.
Write down an expression in term of v,for the time in hour,if the speed is 5 km/h greater
Given that the return journey is 20 minute lesser then the first. Form an equation to show that it simpliflied to v2+5v-750=0
To find the expression for the time Alan took to complete the journey from x to y in terms of v, we can use the formula:
Time = Distance / Speed
In this case, the distance is 50 km. So the expression in terms of v would be:
Time = 50 km / v km/h
To find the expression for the time if the speed is 5 km/h greater, we just need to substitute v with (v + 5) in the above expression:
Time = 50 km / (v + 5) km/h
Now, let's form an equation based on the given information: the return journey is 20 minutes (or 20/60 = 1/3 hours) shorter than the first journey.
Using the first expression for the time (50 km / v km/h) and subtracting 1/3, we get:
50/v - 1/3
Using the second expression for the time (50 km / (v + 5) km/h), we have:
50/(v + 5)
Since the return journey is 20 minutes lesser than the first journey, we can set up the equation:
50/v - 1/3 = 50/(v + 5)
To simplify this equation, we can multiply every term by 3v(v + 5) to remove the fractions:
3v(v + 5) * (50/v) - 3v(v + 5) * (1/3) = 3v(v + 5) * (50/(v + 5))
150(v + 5) - v(v + 5) = 150v
Simplifying further:
150v + 750 - v^2 - 5v = 150v
Combining like terms:
-v^2 + 150v - 5v + 150v - 150v - 750 = 0
Simplifying:
-v^2 + 295v - 750 = 0
And this is the equation simplified to v^2 + 295v - 750 = 0.