a reservation clerk worked 13.5 hours one day. she spent twice as much time entering new reservation as she did verifying old ones and one and a half as much time calling to confirm reservation as verifying old ones. how much time did she spend entering new reservation?
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Let's denote the time spent on entering new reservations as "x".
According to the given information:
The time spent verifying old reservations = x/2
The time spent calling to confirm reservations = (3/2)(x/2) = 3x/4
The total time worked by the reservation clerk is 13.5 hours. So, we can write the equation:
x + x/2 + 3x/4 = 13.5
To solve this equation, we can first find the common denominator:
4x + 2x + 3x = 13.5 * 4
9x = 54
x = 54/9
x = 6
Therefore, the reservation clerk spent 6 hours entering new reservations.
To find out how much time the reservation clerk spent entering new reservations, let's go step by step.
Let's say the time the clerk spent verifying old reservations is X hours.
According to the given information:
- The time spent entering new reservations is twice the time spent verifying old ones.
- The time spent calling to confirm reservations is one and a half times the time spent verifying old ones.
So, the time spent entering new reservations is 2X hours.
The time spent calling to confirm reservations is 1.5X hours.
Now, we know that the total time worked by the clerk is 13.5 hours.
So, the equation we can create for the total time worked is:
X + 2X + 1.5X = 13.5
Combining like terms, we have:
4.5X = 13.5
Dividing both sides by 4.5 to isolate X, we get:
X = 3
Therefore, the time spent entering new reservations is:
2X = 2 * 3 = 6 hours.
So, the reservation clerk spent 6 hours entering new reservations.
if we let
x = entering new reservations
y = verifying old ones
z = confirming
then
x + y + z = 13.5
x = 2y
z = 1.5 y
2y + y + 1.5y = 13.5
4.5y = 13.5
y = 3
so, x = 2y = 6 hours on new reservations.