Maths-
General
Easy

Question

# Solve  The cruising speed of Kennedy's boat is 25 mi/h. She plans to cruise at this speed for the distances shown in the diagram. What equation models the number of hours x that Kennedy will travel ?a. What are the minimum and maximum number of hours kennedy will travel ?

Hint:

## The correct answer is: x=2.8, 3.6

### Step by step solution:The given equation is|3x - 6| = 12Using the definition of absolute value, We get two possibilities,For 3x - 6 < 0,|3x - 6| = -(3x - 6) = 12Simplifying, we get-3x + 6 = 12Subtracting 6 both sides, we have-3x = 12 - 6 = 6Dividing throughout by -3, we getx = -2For 3x - 6 ≥ 0,|3x - 6| = 3x - 6 = 12Adding 6 both sides, we get3x = 12 + 6 = 18Dividing by 3 throughout, we getx = 6Hence, we get two values of x satisfying the given equation,x = -2, 6Given,The number of hours travelled = xCruising speed of Kennedy’s boat = 25 mi/hDistance she plans to travel = 80  10 miWe know,Speed= The above equation can be rewritten asDistance=Speed × TimeWe form an equation in terms of distance travelled by the boat.From the above relation, we haveTotal distance travelled by the boat = 25x miThus, the equation representing the given situation is|25x  -80| = 10We solve the above equation to get two values of x, which will be the minimum and maximum values  of x.Using the definition of absolute value, We get two possibilities,For 25x - 80 < 0,|25x - 80 |= -(25x - 80) = 10Simplifying, we get-25x + 80 = 10Subtracting 80 both sides, we have-25x = 10 - 80 = -70Dividing throughout by -25, we getx = = 2.8For 25x - 80 ≥ 0,|25x - 80| = 25x - 80 = 10Adding 80 both sides, we get25x = 10 + 80 = 90Dividing by 25 throughout, we getx = = 3.6Hence, we get two values of x satisfying the given equation,x=2.8, 3.6Thus,Maximum number of hours Kennedy travels = 3.6 hoursMinimum number of hours Kennedy travels = 2.8 hours

Absolute value of a variable has many uses in mathematics. Geometrically, the absolute value of a number may be considered as its distance from zero regardless of its direction. The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘mod x’.