A motor cyclist makes a trip of 500km. If he had increased his speed by 10kmh-1, he could have covered 600km in the same time. What was the original speed?

the original speed is 50 km/h

Step-by-step explanation:

Let us assume the original speed be x

and fastest speed be (x+ 10)

Now here apply the time formula

i.e. distance by the speed

Original time = Fastest time

500 ÷ x = 600 ÷ x + 10

Now do cross multiplication

600x = 500(x + 10)

600x = 500x + 5000

100x = 5000

x = 50 km/h

Hence, the original speed is 50 km/h

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions