Maths-
General
Easy

Question

# Write and solve an absolute value equation for the minimum and maximum times for an object moving at the given speed to travel the given distance.

Hint:

## The correct answer is: Hence, we get two values of x satisfying the given equation, x=0.75, 1.25

### Step by step solution:Given,Let the number of hours travelled be xSpeed of the object = 10 mi/hDistance she plans to travel = 10  2.5 miWe know, The above equation can be rewritten as We form an equation in terms of distance travelled by the boat.From the above relation, we haveTotal distance travelled by the boat = 10x  miThus, the equation representing the given situation is|10x-10| = 2.5We 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 10x-10<0,Simplifying, we get- 10 x + 10 = 2.5Dividing by 10 throughout, we get Hence, we get two values of x satisfying the given equation,x = 0.75, 1.25Thus,Maximum number of hours travelled = 1.25 hoursMinimum number of hours travelled = 0.75 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’.