Chapter 11 QuaDraTiC appliCaTionS 403(^6565)
6306 5
12 30 5
0
2
2
2
()tttt()
tttt
ttt
t
++=+
++=+
+=+
=− 7730
0103
t
tt
−
=−()()+
t − 10 = 0 t + 3 = 0 (This does not lead to a solution.)
t = 10
Alex can peel the potatoes in 10 minutes and Tina can peel them in
10 + 5 = 15 minutes.
- Let t represent the number of minutes Jared needs to wash the car by
himself. The time Rachel needs to wash the car by herself is t + 24.
Worker Quantity Rate Time
Jared 1 1
ttRachel (^1) t+^124 t + 24
Together 1 1
16
16
The equation to solve is^11
24
1
tt 16
+ .
+
= The LCD is 16t(t + 24).
11
24
1
16
16 24 1 16 24 1
24
16
tt
tt
t
tt
t
tt
=
+⋅++⋅
() () =+( 224 1
16
16 24 16 24
16 384 16 24
3
2
)
() ()
⋅
++=+
++=+
tttt
tttt
22 384 24
08384
02416
2
2
ttt
tt
tt
+=+
=−−
=−()()+
t − 24 = 0 t + 16 = 0 (This does not lead to a solution.)
t = 24
Jared needs 24 minutes to wash the car alone and Rachel needs 24 + 24 =
48 minutes.