If a family spends $12.75 for tickets to the fair and gives the cashier a $20 bill, how much change will be returned?
1 answer:
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Speed of the east bound cyclist is 12 mph and the speed of west bound cyclist is 15 mph.
<u>Solution:</u>
Let us assume that x is speed of slower eastbound cyclist
So, x+3 will be the speed of faster westbound cyclist
We know that distance is the product of speed and time. That is,
West-bound DATA:
Rate of speed = x+3 mph ; Time = 6 hrs ; distance = 6(x+3) = 6x+18 miles
East-bound DATA:
Rate of speed = x mph ; time = 6 hrs. ; distance = 6x miles
On solving,
Distance apart = 162
So, the rate of speed of the east bound cyclist is 12 mph and the rate of speed of the west bound cyclist will be
Answer:
The system of equations has a one unique solution
Step-by-step explanation:
To quickly determine the number of solutions of a linear system of equations, we need to express each of the equations in slope-intercept form, so we can compare their slopes, and decide:
1) if they intersect at a unique point (when the slopes are different) thus giving a one solution, or
2) if the slopes have the exact same value giving parallel lines (with no intersections, and the y-intercept is different so there is no solution), or
3) if there is an infinite number of solutions (both lines are exactly the same, that is same slope and same y-intercept)
So we write them in slope -intercept form:
First equation:
second equation:
So we see that their slopes are different (for the first one slope = -6, and for the second one slope= -3/2) and then the lines must intercept in a one unique point. Therefore the system of equations has a one unique solution.