Two Features, One Matrix Inverse

A courier dispatcher models delivery time from two features:

The model carries no bias term:

$\hat{y} = w_1 x_1 + w_2 x_2$

Four completed deliveries make up the training set:

Delivery	Items $x_1$	Distance $x_2$ (km)	Time $y$ (min)
1	$1$	$2$	$7$
2	$2$	$1$	$5$
3	$3$	$4$	$12$
4	$4$	$3$	$16$

The design matrix $X$ is $4 \times 2$ — its two columns are $x_1$ and $x_2$ — and the least-squares weights are the solution of the normal equations

$X^\top X\, \hat{w} = X^\top y$

A new order comes in: $6$ items, $5$ km away.

What delivery time does the fitted model predict for it?

Round your answer to two decimal places.