Question

Suzette ran and biked for a total of 44.75 mi in 4 h. Her average running speed was 6.5 mph and

Answer 1

The total hours Suzette biked was 2.5 hours and she ran for 1.5 hours

Let x = total hours Suzette ran.

Let y = total hours Suzette biked

The equation to solve the question will be:

x + y = 4 ....... equation i

6.5x + 14y = 44.75 ........ equation ii

From equation i, x = 4 - y ....... iii

Put the value of x into equation ii

6.5x + 14y = 44.75

6.5(4 - y) + 14y = 44.75

26 - 6.5y + 14y = 44.75

Collect like terms

-6.5y + 14y = 44.75 - 26

7.5y = 18.75

Divide through by 7.5

7.5y/7.5 = 18.75/7.5

y = 2.5

Since x + y = 4

x + 2.5 = 4

x = 4 - 2.5

x = 1.5

Suzette ran for 1.5 hours

In conclusion, the total hours Suzette biked was 2.5 hours and she ran for 1.5 hours.

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Answer 2

From the information given:

Suzette ran and biked for a total of 44.75 ml in 4 hours.

Let us assume that:

• x = to the total time that Suzette use to ran
• y = to the total time Suzette use to bike

Then;

(a)

the system of the two equations can be expressed as:

x     +   y     = 4               ------ (1)

6.5x + 14y = 44.75        ------- (2)

(b)

Using substitution method:

From equation (1), let's make (x) the subject of the formula, so:

x = 4 - y

Replace the value of x into equation (2), we have:

6.5(4-y) + 14 y = 44.75

Open brackets

26 - 6.5y + 14y = 44.75

26 + 7.5y = 44.75

7.5y = 44.75 - 26

7.5y = 18.75

y = 18.75/7.5

y = 2.5

Now, since the value of y is known, then, we can replace it back into equation ((1) to solve for (X);

SO;

x + y = 4

x = 4 - y

x = 4 - 2.5

x = 1.5

Thus, We can say that:

• Suzette ran for x hours = 1.5 hours
• Suzette bike for y hours = 2.5 hours

To check by substituting the value of x and y into the equation:

The purpose of checking is to make sure that what we have on the right-hand side is equivalent to what is on the left-hand side.

So:

Using equation (1)

x + y = 4

2.5  + 1.5 = 4

4 = 4

We can therefore conclude that Suzette ran for 1.5 hours and biked for 2.5 hours.

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