Answer:
The average speed on Monday is 27mph
Step-by-step explanation:
Given
Let:
[tex]1\to Sunday[/tex]
[tex]2\to Monday[/tex]
So:
[tex]t_1 = 5.4hr[/tex]
[tex]t_2 = 6hr[/tex]
[tex]s_2 = s_1 - 3[/tex] ---- average speed slower on Monday than Tuesday
Required
The average speed on Monday
Average speed is calculated as:
[tex]Speed = \frac{Distance}{Time}[/tex]
[tex]s = \frac{d}{t}[/tex]
Make d the subject
[tex]d = st[/tex]
On Sunday, we have:
[tex]d = s_1t_1[/tex]
[tex]d = s_1 * 5.4[/tex]
On Monday, we have:
[tex]d = s_2t_2[/tex]
[tex]d = s_2 * 6[/tex]
The distance traveled is constant;
So:
[tex]s_1 * 5.4 = s_2 * 6[/tex]
Make s1 the subject in: [tex]s_2 = s_1 - 3[/tex]
[tex]s_1=3+s_2[/tex]
So, we have:
[tex](3 + s_2) * 5.4 = s_2 * 6[/tex]
Open bracket
[tex]16.2 + 5.4s_2 = 6s_2[/tex]
Collect like terms
[tex]6s_2 - 5.4s_2 = 16.2[/tex]
[tex]0.6s_2 = 16.2[/tex]
Solve for s_2
[tex]s_2 = 16.2/0.6[/tex]
[tex]s_2 = 27[/tex]
The average speed on Monday is 27mph
